1. Convert 100 K into temperature on Fahrenheit scale?
2. At what temperature does Kelvin scale reading coincide with Fahrenheit scale? [ Ans: 574.25 K ]
3. At what temperature will the Kelvin scale reading double the Fahrenheit reading? [ Ans: 353.4 K or 176.7 0F ]
4. A faulty thermometer has its fixed points marked at -2 and 98. What is the correct temperature on Celsius scale when the thermometer reads 20 0C ? [Ans: 22 0C]
5. At what temperature will the reading of a Fahrenheit thermometer be double than that of the centigrade one? [ Ans: 160 0C or 320 0F]
6. What fall of temperature will the Fahrenheit thermometer register, when the centigrade thermometer records the fall in temperature as 45 0C? [ Ans: 81 0F ]
7. A faulty Fahrenheit thermometer shows 204 0F, whereas a centigrade thermometer registers 95 0C. Find the correction for faulty thermometer? [ Ans: 1 0F ]
8. If a centigrade thermometer reads 370 when a standard Fahrenheit thermometer reads 100o. What is the error in centigrade thermometer? [ Ans: 0.77o ]
9. A faulty thermometer measures the temperature of an object as 28.2 0C. The UFP an LFP of thermometers are 98.4 0C and -1.2 0C respectively. What is the correct temperature of object? [Ans: 29.51 0C ]
10. In an arbitrary scale of temperature, water freezes at 40 0C and boils at 290 0C. Find the boiling point of liquid in this scale if it boils at 62 0C? [ Ans: 195 0C ]
11. The difference between UFP and LFP is 80 cm. Find the temperature on the Celsius scale if the mercury level rises to a height 10.4 cm above LFP? [ Ans: 13 0C ]
12. A platinum resistance thermometer reads 0 0C when R = 80 Ω and 100 0C when R = 90 Ω. Find the temperature of the platinum scale at which R = 86 Ω? [ Ans: 60 0C]
13. Water boils at 100 0C at normal atmospheric pressure. The atmospheric pressure of KTM is 64.5 mm of Hg.
(i) At what temperature would water boil in Kathmandu? [ Ans: 95.7 0C ]
(ii) At what pressure would water boil at 150 0C? [ Ans: 2.8 atm. ]
14. A 0C and 0F thermometer are placed in hot water. The water is then cooled. What fall of temperature will the Fahrenheit thermometer register, when the centigrade thermometer records the fall in temperature as 45 0C. [ Ans: 81 0F ]
15. A faulty thermometer reads - 20 0C in melting ice and 102 0C in steam at normal pressure (a) what is the correct temperature when the faulty thermometer reads 20 0C? (b) What the faulty thermometer read when the correct temperature is 20 0C? (c) At what temperature is its reading exactly correct? [ Ans: 21.2 0C, 18.8 0C, 50 0C ]
14. A 0C and 0F thermometer are placed in hot water. The water is then cooled. What fall of temperature will the Fahrenheit thermometer register, when the centigrade thermometer records the fall in temperature as 45 0C. [ Ans: 81 0F ]
15. A faulty thermometer reads - 20 0C in melting ice and 102 0C in steam at normal pressure (a) what is the correct temperature when the faulty thermometer reads 20 0C? (b) What the faulty thermometer read when the correct temperature is 20 0C? (c) At what temperature is its reading exactly correct? [ Ans: 21.2 0C, 18.8 0C, 50 0C ]
Thermal expansion
1. A copper length of 3 m is heated from 30 0C to 80 0C. If its length increases by 2.55mm, calculate the coefficient of linear expansion of copper? [ Ans: 17 x 10-6 0C-1 ]
2. The length of rod increases by 0.2 % when heated through 100 0C. Calculate the coefficient of linear expansion of rod? [ Ans: 2 x 10-5 0C-1 ]
3. The side of a brass cube is 10 cm at 15 0C. If it is heated, calculate its side and volume at 60 0C. Coefficient of linear expansion of brass = 1.9 x 10-5 0C-1. [ Ans: 10.0085 cm, 1002.5 cm3 ]
4. A thin copper wire of length L increases in length by 1 % when heated from temperature T1 to T2. What will be the change in area when a thin copper plate of dimensions 2L x L is heated from T1 to T2?[ Ans: 2 % ]
5. A steel rod when measured with a zinc scale both being at 25 0C appear to be one meter long. If the zinc scale is correct at 0 0C, what is the actual length of rod at 25 0C? What will be the length of rod at 0 0C? linear expansivity of steel = 12 x 10-6 0C-1, linear expansivity for zinc = 26 x 10-6 0C-1 [ Ans: 1.00065 m, 1.00035m ]
6. A blacksmith fixes iron ring on a wooden wheel of a bullock cart. The diameter of wheel and the iron ring are 5.243 m and 5.231 m respectively at 27 0C. To what temperature should the ring be heated so as to fit the ring on the wheel. ( αiron = 1.20 x 10-5 0C-1 )[ Ans: 218.2 0C ]
7. A brass rod and a steel rod differ by 10 cm in length at all temperatures. What are their lengths at 0 0C? ( αbrass = 18 x 10-6/0C, αsteel = 12 x 10-6/0C ) [ Ans: 20 cm and 30 cm ]
8. The distance between the two points A and B is 625 Km. Find the total space that must be left between the iron rails to allow for a change of temperature from 36 0F in winter to 117 0F in summer? ( αiron = 12 x 10-6/0C) [ Ans: 337.5 m]
9. A steel rod and a brass rod when measured at 0 0C are 50.1 cm and 50.0 cm respectively. At what temperature will their lengths equal and what will be their common length? ( αsteel = 12 x 10-6/0C, αbrass = 18 x 10-6/0C) [ Ans: 334.67 0C]
10. The marking on an aluminum ruler and a brass ruler are perfectly aligned at 0 0C. How far apart will the 20.0 cm marks be on the two rulers at 100 0C, if precise alignment of the left hand ends of the rulers is maintained? (αaluminum = 2.4 x 10-5/0C and αbrass = 2 x 10-5/0C) [ Ans: 8 x 10-5 m ]
11. A steel tape is correctly calibrated at 10 0C. It is used at a temperature of 30 0C to measure the distance between two lines on a cement floor. The reading obtained is 4.0 m. What is the actual distance between the lines? (αsteel = 12 x 10-6/0C) [ Ans: 4.00096 m ]
12. The length of an iron rod measured by a brass scale. When both of them are at 10 0C, the measured length is 50 cm. what is the length of rod at 40 0C when measured by the brass scale at 40 0C? (αbrass = 24 x 10-6/0C, αiron = 16 x 10-6/0C) [ Ans: 49.98 cm ]
13. A copper wire of diameter 0.5 mm is stretched between two points at 25 0C. Calculate the increase in tension in the wire if the temperature falls to 0 0C. (αcopper = 18 x 10-6/0C and Young’s modulus of elasticity for copper = 1.2 x 1011 Nm-2) [ Ans: 10.6 N]
14. A brass rod is 185 cm long and 1.60 cm in diameter. What force must be applied to each end of the rod to prevent it from contracting when it is cooled from 120 0C to 10 0C? (αbrass = 18 x 10-6/0C) [ Ans: 36625.4 N ]
15. The pendulum of a clock is made of brass whose linear expansivity is 1.9 x 10-5/K. If the clock keeps correct time at 15 0C, how many seconds per day will it loose at 20 0C? [Ans: 4.1s]
16. A pendulum clock gives correct time at 20 0C. How many seconds a day will it gain or loose when the temperature falls to 5 0C? (αpendulum = 0.0002/0C) [ Ans: 129.6 secs ]
17. A circular hole of radius 1 cm in a brass sheet is kept at 293 K. What will be the diameter of this hole when the temperature of sheet is increased by 100 K. (α brass = 20 x 10-6/0C) [Ans: 2.004 cm ]
18. A steel tape measures accurately at 20 0C. It is used at 10 0C to measure a kilometer distance. What reading will the tape show? (αsteel = 12 x 10-6/0C) [ Ans: 1000.12 Km ]
19. A steel wire 8 m long and 4 mm in diameter is fixed to two rigid supports. Calculate the increase in tension when the temperature falls by 10 0C. (αsteel = 12 x 10-6/0C, Ysteel = 2 x 1011 Nm-2) [Ans: 301.6 N]
20. A steel cylinder has an aluminum alloy piston ans at a temperature of 20 0C when the internal diameter of a cylinder is exactly 10 cm, there is an all round clearance of 0.05 mm between the piston and the cylinder wall. At what temperature will the fit be perfect? (αsteel = 12 x 10-6/0C, αaluminum = 16 x 10-6/0C ) [ Ans: 272 0C ]
1. A copper length of 3 m is heated from 30 0C to 80 0C. If its length increases by 2.55mm, calculate the coefficient of linear expansion of copper? [ Ans: 17 x 10-6 0C-1 ]
2. The length of rod increases by 0.2 % when heated through 100 0C. Calculate the coefficient of linear expansion of rod? [ Ans: 2 x 10-5 0C-1 ]
3. The side of a brass cube is 10 cm at 15 0C. If it is heated, calculate its side and volume at 60 0C. Coefficient of linear expansion of brass = 1.9 x 10-5 0C-1. [ Ans: 10.0085 cm, 1002.5 cm3 ]
4. A thin copper wire of length L increases in length by 1 % when heated from temperature T1 to T2. What will be the change in area when a thin copper plate of dimensions 2L x L is heated from T1 to T2?[ Ans: 2 % ]
5. A steel rod when measured with a zinc scale both being at 25 0C appear to be one meter long. If the zinc scale is correct at 0 0C, what is the actual length of rod at 25 0C? What will be the length of rod at 0 0C? linear expansivity of steel = 12 x 10-6 0C-1, linear expansivity for zinc = 26 x 10-6 0C-1 [ Ans: 1.00065 m, 1.00035m ]
6. A blacksmith fixes iron ring on a wooden wheel of a bullock cart. The diameter of wheel and the iron ring are 5.243 m and 5.231 m respectively at 27 0C. To what temperature should the ring be heated so as to fit the ring on the wheel. ( αiron = 1.20 x 10-5 0C-1 )[ Ans: 218.2 0C ]
7. A brass rod and a steel rod differ by 10 cm in length at all temperatures. What are their lengths at 0 0C? ( αbrass = 18 x 10-6/0C, αsteel = 12 x 10-6/0C ) [ Ans: 20 cm and 30 cm ]
8. The distance between the two points A and B is 625 Km. Find the total space that must be left between the iron rails to allow for a change of temperature from 36 0F in winter to 117 0F in summer? ( αiron = 12 x 10-6/0C) [ Ans: 337.5 m]
9. A steel rod and a brass rod when measured at 0 0C are 50.1 cm and 50.0 cm respectively. At what temperature will their lengths equal and what will be their common length? ( αsteel = 12 x 10-6/0C, αbrass = 18 x 10-6/0C) [ Ans: 334.67 0C]
10. The marking on an aluminum ruler and a brass ruler are perfectly aligned at 0 0C. How far apart will the 20.0 cm marks be on the two rulers at 100 0C, if precise alignment of the left hand ends of the rulers is maintained? (αaluminum = 2.4 x 10-5/0C and αbrass = 2 x 10-5/0C) [ Ans: 8 x 10-5 m ]
11. A steel tape is correctly calibrated at 10 0C. It is used at a temperature of 30 0C to measure the distance between two lines on a cement floor. The reading obtained is 4.0 m. What is the actual distance between the lines? (αsteel = 12 x 10-6/0C) [ Ans: 4.00096 m ]
12. The length of an iron rod measured by a brass scale. When both of them are at 10 0C, the measured length is 50 cm. what is the length of rod at 40 0C when measured by the brass scale at 40 0C? (αbrass = 24 x 10-6/0C, αiron = 16 x 10-6/0C) [ Ans: 49.98 cm ]
13. A copper wire of diameter 0.5 mm is stretched between two points at 25 0C. Calculate the increase in tension in the wire if the temperature falls to 0 0C. (αcopper = 18 x 10-6/0C and Young’s modulus of elasticity for copper = 1.2 x 1011 Nm-2) [ Ans: 10.6 N]
14. A brass rod is 185 cm long and 1.60 cm in diameter. What force must be applied to each end of the rod to prevent it from contracting when it is cooled from 120 0C to 10 0C? (αbrass = 18 x 10-6/0C) [ Ans: 36625.4 N ]
15. The pendulum of a clock is made of brass whose linear expansivity is 1.9 x 10-5/K. If the clock keeps correct time at 15 0C, how many seconds per day will it loose at 20 0C? [Ans: 4.1s]
16. A pendulum clock gives correct time at 20 0C. How many seconds a day will it gain or loose when the temperature falls to 5 0C? (αpendulum = 0.0002/0C) [ Ans: 129.6 secs ]
17. A circular hole of radius 1 cm in a brass sheet is kept at 293 K. What will be the diameter of this hole when the temperature of sheet is increased by 100 K. (α brass = 20 x 10-6/0C) [Ans: 2.004 cm ]
18. A steel tape measures accurately at 20 0C. It is used at 10 0C to measure a kilometer distance. What reading will the tape show? (αsteel = 12 x 10-6/0C) [ Ans: 1000.12 Km ]
19. A steel wire 8 m long and 4 mm in diameter is fixed to two rigid supports. Calculate the increase in tension when the temperature falls by 10 0C. (αsteel = 12 x 10-6/0C, Ysteel = 2 x 1011 Nm-2) [Ans: 301.6 N]
20. A steel cylinder has an aluminum alloy piston ans at a temperature of 20 0C when the internal diameter of a cylinder is exactly 10 cm, there is an all round clearance of 0.05 mm between the piston and the cylinder wall. At what temperature will the fit be perfect? (αsteel = 12 x 10-6/0C, αaluminum = 16 x 10-6/0C ) [ Ans: 272 0C ]
Liquid expansion
1. Using the following data, determine the temperature at which wood will just sink in benzene. Density of benzene at 0 0C = 9 x 102 Kg/m3, density of wood at 0 0C = 8.8 x 102 Kg/m3, cubical expansivity of benzene and wood are 1.2 x 10-3 /K and 1.5 x 10-4 /K respectively. [Ans: 21.7 0C]
2. A glass flask with volume 200 cm3 is filled with mercury at 20 0C. How much mercury overflows when the temperature of the system raised to 100 0C? (αglass = 4 x 10-6/0C, γmercury = 18 x 10-5/0C) [Ans: 2.7 x 10-6 m3]
3. A piece of steel floats in mercury at 0 0C with 57.35 % of its volume submerged. What percentage of its volume will be submerged when the temperature is raised through 50 0C? ( relative densities of steel and mercury are 7.8 and 13.6 respectively, αsteel = 12 x 10-6/0C and γmercury = 18 x 10-5/0C) [ Ans: 57.7 % ]
4. A copper vessel with a volume exactly 1.80 m3 at a temperature 20 0C is filled with glycerin. If the temperature rises to 30 0C, how much glycerin will spill out? (αcopper = 16.7 x 10-6/0C, γglycerin = 5.3 x 10-4/0C) [ Ans: 0.00864 m3 ]
5. A glass flask whose volume is exactly 1000 cm3 at 0 0C is filled full of mercury at this temperature. When flask and mercury are heated to 100 0C, 15.2 cm3 of mercury overflows. If the cubical expansivity of mercury is 0.000182 0C-1. Compute the linear expansivity of the glass. [ Ans: 1.0 x 10-5 0C-1 ]
6. In an experiment performed by Dulong and Petit’s method the height of the cold and hot columns of mercury are found to be 99.5 cm and 101.2 cm respectively. If the temperature of cold column is 0 0C, calculate the temperature of hot column. (γmercury = 18 x 10-5/0C) [ Ans: 94.92 0C ]
7. The density of silver at 0 0C is 10310 Kgm-3 and the coefficient of linear expansion is 0.000019 0C-1, calculate its density at 100 0C. [ Ans: 10251.56 Kgm-3 ]
8. How much glycerin must be placed inside a glass vessel of capacity 250 cc, so that volume of the space unoccupied by glycerin always remains constant? (γglycerin = 53 x 10-5/0C, αglass = 9 x 10-6 /0C) [ Ans: 12.73 cc ]
9. A copper cylinder is initially at 20 0C. At what temperature will its volume be 0.150 % larger than it is at 20.0 0C? (αcopper = 16.7 x 10-6 /0C) [ Ans: 109.5 0C ]
10. A piece of glass weighs 25 g in air, 16.77 g in water at 4 0C and 16.89 g in water at 60 0C. Find the mean coefficient of cubical expansion of water between 4 0C and 60 0C, taking the coefficient of linear expansion of glass as 8 x 10-6 K-1. [ Ans: 2.885 x 10-4 K-1 ]
11. A glass vessel is completely filled with 340 gm of mercury at 0 0C. What weight of mercury will overflow when the vessel is heated to 100 0C? (γmercury = 18 x 10-5/0C, αglass = 9 x 10-6/0C) [ Ans: 5.11 gm ]
12. A glass vessel contains some tungsten balls and is then filled with mercury to a certain mark. It is found that the mercury level always remains at this mark when the glass vessel is heated. What is the ratio of volume of Hg to that of tungsten at 0 0C. (γmercury = 18 x 10-5/0C, αglass = 8 x 10-6/0C and αtungsten = 4.4 x 10-6/0C) [ Ans: 9/130 or 0.069]
13. A silica bulb of negligible expansivity holds 340 gm of mercury at 0 0C when full. Some steel balls are introduced and the remaining space is occupied at 0 0C by 255.0 gm of mercury. On heating the bulb and its contents to 100 0C, 4.800 gm of mercury overflows. Find the linear expansivity of steel. (γmercury = 18 x 10-5/ K) [ Ans: 11.6 x 10-6 /K]
14. A glass vessel contains when full 544 gm of mercury at 0 0C. The mass of mercury which fills it at 100 0C is 535.45 gm. Calculate the cubical expansivity of glass. (γmercury = 18 x 10-5/K) [ Ans: 2 x 10-5 /K ]
1. Using the following data, determine the temperature at which wood will just sink in benzene. Density of benzene at 0 0C = 9 x 102 Kg/m3, density of wood at 0 0C = 8.8 x 102 Kg/m3, cubical expansivity of benzene and wood are 1.2 x 10-3 /K and 1.5 x 10-4 /K respectively. [Ans: 21.7 0C]
2. A glass flask with volume 200 cm3 is filled with mercury at 20 0C. How much mercury overflows when the temperature of the system raised to 100 0C? (αglass = 4 x 10-6/0C, γmercury = 18 x 10-5/0C) [Ans: 2.7 x 10-6 m3]
3. A piece of steel floats in mercury at 0 0C with 57.35 % of its volume submerged. What percentage of its volume will be submerged when the temperature is raised through 50 0C? ( relative densities of steel and mercury are 7.8 and 13.6 respectively, αsteel = 12 x 10-6/0C and γmercury = 18 x 10-5/0C) [ Ans: 57.7 % ]
4. A copper vessel with a volume exactly 1.80 m3 at a temperature 20 0C is filled with glycerin. If the temperature rises to 30 0C, how much glycerin will spill out? (αcopper = 16.7 x 10-6/0C, γglycerin = 5.3 x 10-4/0C) [ Ans: 0.00864 m3 ]
5. A glass flask whose volume is exactly 1000 cm3 at 0 0C is filled full of mercury at this temperature. When flask and mercury are heated to 100 0C, 15.2 cm3 of mercury overflows. If the cubical expansivity of mercury is 0.000182 0C-1. Compute the linear expansivity of the glass. [ Ans: 1.0 x 10-5 0C-1 ]
6. In an experiment performed by Dulong and Petit’s method the height of the cold and hot columns of mercury are found to be 99.5 cm and 101.2 cm respectively. If the temperature of cold column is 0 0C, calculate the temperature of hot column. (γmercury = 18 x 10-5/0C) [ Ans: 94.92 0C ]
7. The density of silver at 0 0C is 10310 Kgm-3 and the coefficient of linear expansion is 0.000019 0C-1, calculate its density at 100 0C. [ Ans: 10251.56 Kgm-3 ]
8. How much glycerin must be placed inside a glass vessel of capacity 250 cc, so that volume of the space unoccupied by glycerin always remains constant? (γglycerin = 53 x 10-5/0C, αglass = 9 x 10-6 /0C) [ Ans: 12.73 cc ]
9. A copper cylinder is initially at 20 0C. At what temperature will its volume be 0.150 % larger than it is at 20.0 0C? (αcopper = 16.7 x 10-6 /0C) [ Ans: 109.5 0C ]
10. A piece of glass weighs 25 g in air, 16.77 g in water at 4 0C and 16.89 g in water at 60 0C. Find the mean coefficient of cubical expansion of water between 4 0C and 60 0C, taking the coefficient of linear expansion of glass as 8 x 10-6 K-1. [ Ans: 2.885 x 10-4 K-1 ]
11. A glass vessel is completely filled with 340 gm of mercury at 0 0C. What weight of mercury will overflow when the vessel is heated to 100 0C? (γmercury = 18 x 10-5/0C, αglass = 9 x 10-6/0C) [ Ans: 5.11 gm ]
12. A glass vessel contains some tungsten balls and is then filled with mercury to a certain mark. It is found that the mercury level always remains at this mark when the glass vessel is heated. What is the ratio of volume of Hg to that of tungsten at 0 0C. (γmercury = 18 x 10-5/0C, αglass = 8 x 10-6/0C and αtungsten = 4.4 x 10-6/0C) [ Ans: 9/130 or 0.069]
13. A silica bulb of negligible expansivity holds 340 gm of mercury at 0 0C when full. Some steel balls are introduced and the remaining space is occupied at 0 0C by 255.0 gm of mercury. On heating the bulb and its contents to 100 0C, 4.800 gm of mercury overflows. Find the linear expansivity of steel. (γmercury = 18 x 10-5/ K) [ Ans: 11.6 x 10-6 /K]
14. A glass vessel contains when full 544 gm of mercury at 0 0C. The mass of mercury which fills it at 100 0C is 535.45 gm. Calculate the cubical expansivity of glass. (γmercury = 18 x 10-5/K) [ Ans: 2 x 10-5 /K ]
Quantity of heat
1. A metal piece of mass 250 gm at 80 0C is dropped into 120 gm water at 20 0C. Find the final temperature reached, if the specific heat capacity of metal is 0.09 cal gm-1 0C-1. [Ans: 29.5 0C]
2. A piece of copper weighing 15 gm was heated to 100 0C. It was dropped to a copper calorimeter of mass 60 gm containing 44 gm of water at 20 0C. What is the resulting temperature? (Scopper = 0.094 ca/gm0C) [ Ans: 22.2 0C ]
3. A metal of mass 25 gm at temperature of 100 0C, is dropped into calorimeter containing 200 gm of water initially at 20 0C. The final temperature is 22 0C. Compute specific heat capacity of the metal if the water equivalent of the calorimeter is 10 gm. [ Ans: 0.21 Cal/gm0C-1 ]
4. A piece of lead weighing 50 gm is heated in boiling water, then quickly transferred to a copper calorimeter of mass 40 gm containing 50 gm of water at 15 0C. After stirring the final steady temperature is found to be 17.2 0C. Calculate the temperature of the boiling water. (Scopper = 400 J/Kg K and Slead = 127 J/Kg K) [ Ans: 95.5 0C]
5. Equal volumes of two liquids have the same heat capacity. The relative density of one liquid is 0.87 and that of another is 0.70. If the specific heat capacity of the first liquid is 1.813 Jgm-1K-1, find the specific heat capacity of second liquid. [ Ans: 2.25 Jgm-1K-1 ]
6. A ball of copper weighing 400 gm is transferred from a furnace to a copper calorimeter of mass 300 gm and containing 1 Kg of water at 20 0C. The temperature of water rises to 50 0C. What is the original temperature of the ball? (Scopper = 400 JKg-1K-1 and Swater = 4200 JKg-1K-1) [ Ans: 837.5 0C]
7. A piece of copper of mass 15 gm held in a flame until it has acquired the temperature of the flame. It is then quickly transferred to a copper calorimeter of mass 66 gm containing 50 gm of water at 20 0C. If the final steady temperature of the calorimeter and its contents is 27.5 0C. Calculate the temperature of flame. (Scopper = 0.4 J/gm0C) [ Ans: 323 0C ]
8. A calorimeter was filled with 50 gm of water at 15 0C. A copper ball of mass 40 gm and temperature 100 0C is dropped into the calorimeter. The final temperature is 20 0C. What would be the final temperature, if instead of copper ball, a silver ball of same mass and temperature were dropped to the calorimeter? ( specific heat capacity of copper, silver and water are 400 J/KgK, 230 J/KgK and 4200 J/KgK respectively) [ Ans: 17.9 0C ]
9. A copper pot with mass 0.5 Kg contains 0.170 Kg of water at a temperature of 20 0C. A 0.250 Kg block of iron at 85 0C is dropped into the pot. Find the final temperature assuming no heat loss to the surroundings? ( specific heat capacity of copper, water and iron are 390 J/KgK, 4190 J/KgK and 470 J/KgK respectively) [ Ans: 27.5 0C ]
10. Two identical calorimeters are each of heat capacity 12 J/K, one contains 8 x 10-5 m3 of water and takes 150 sec to cool from 325 K to 320 K and the other contains an equal volume of an unknown liquid which takes 50 sec to cool over the same range of temperature if the density of liquid is 800 Kgm-3. What is the average specific heat capacity of liquid over the temperature range? ( density of water = 1000 Kgm-3, specific heat capacity of water = 4200 JKg-1K-1 ) [ Ans: 1625 JKg-1K-1]
11. A substance takes 3 min in cooling from 50 0C to 45 0C and takes 5 min in cooling from 45 0C to 40 0C. What is the temperature of the surroundings? How much time will it take to cool this substance from 40 0C to 35 0C? [ Ans: 35 0C, 15 min]
12. The temperature of body falls from 40 0C to 36 0C in 5 minutes. Find the time taken for the temperature of the body to become 32 0C. The temperature of surrounding is 16 0C. [ Ans: 6.1 minutes]
13. A copper calorimeter weighing 53.2 gm is first filled with water then with a liquid. Time taken to cool from 40 0C to 32 0C in the two cases is 4 min and 3 min respectively. The mass of water is 25 gm and that of liquid is 30 gm. Calculate the specific heat capacity of the liquid? ( specific heat capacity of copper = 0.094 cal/gm0C)[ Ans: 0.58 cal/gm0C]
14. During the flu a 80 Kg man ran a fever of 39 0C instead of the normal body temperature of 37 0C. Assuming the human body is mostly made of water, how much heat is required to raise his temperature by that amount? [ Ans: 67200 J ]
15. A copper sphere of mass m falls from height 90 m. If on reaching the ground 75 % of energy is converted into heat, calculate the rise in temperature of sphere. ( sp heat capacity of copper = 0.1 cal/gm0C) [ Ans: 1.60 0C]
16. In a physics lab experiment a student immersed 200 coins (each having mass of 3 gm) in boiling water. After they reached thermal equilibrium, she fished them out and dropped them into 0.240 kg of water at 20 0C in an insulated container of negligible mass. What was the final temperature of the coin? (sp. heat capacity of coin = 390 J/KgK) [ Ans: 35.07 0C ]
17. A nail driven into a board increases in temperature. If we assume that 60 % of the kinetic energy delivered by a 1.80 Kg hammer with a speed of 7.80 m/s is transformed into heat that flows into the nail and does not flow out, what is the temperature increase in 8.00 gm aluminum nail after it is struck ten times? ( specific heat capacity of aluminum = 910 J/KgK) [ Ans: 45.12 0C]
18. The specific gravity of one liquid is 0.7 and that of another liquid is 0.4. Thermal capacity of 4 litres of first liquid and that of 3 litres of second liquid are equal. Calculate the ratio of specific heat capacities of liquids? [ Ans: 1:1 ]
19. There are three liquids A, B and C having equal masses. Their temperatures are respectively 14 0C, 24 0C and 40 0C. When A and B are mixed, the temperature of the mixture becomes 20 0C; when B and C are mixed, the temperature of the mixture becomes 34 0C. What should be the temperature of the mixture when all the liquids are mixed? [ Ans: 30 0C]
1. A metal piece of mass 250 gm at 80 0C is dropped into 120 gm water at 20 0C. Find the final temperature reached, if the specific heat capacity of metal is 0.09 cal gm-1 0C-1. [Ans: 29.5 0C]
2. A piece of copper weighing 15 gm was heated to 100 0C. It was dropped to a copper calorimeter of mass 60 gm containing 44 gm of water at 20 0C. What is the resulting temperature? (Scopper = 0.094 ca/gm0C) [ Ans: 22.2 0C ]
3. A metal of mass 25 gm at temperature of 100 0C, is dropped into calorimeter containing 200 gm of water initially at 20 0C. The final temperature is 22 0C. Compute specific heat capacity of the metal if the water equivalent of the calorimeter is 10 gm. [ Ans: 0.21 Cal/gm0C-1 ]
4. A piece of lead weighing 50 gm is heated in boiling water, then quickly transferred to a copper calorimeter of mass 40 gm containing 50 gm of water at 15 0C. After stirring the final steady temperature is found to be 17.2 0C. Calculate the temperature of the boiling water. (Scopper = 400 J/Kg K and Slead = 127 J/Kg K) [ Ans: 95.5 0C]
5. Equal volumes of two liquids have the same heat capacity. The relative density of one liquid is 0.87 and that of another is 0.70. If the specific heat capacity of the first liquid is 1.813 Jgm-1K-1, find the specific heat capacity of second liquid. [ Ans: 2.25 Jgm-1K-1 ]
6. A ball of copper weighing 400 gm is transferred from a furnace to a copper calorimeter of mass 300 gm and containing 1 Kg of water at 20 0C. The temperature of water rises to 50 0C. What is the original temperature of the ball? (Scopper = 400 JKg-1K-1 and Swater = 4200 JKg-1K-1) [ Ans: 837.5 0C]
7. A piece of copper of mass 15 gm held in a flame until it has acquired the temperature of the flame. It is then quickly transferred to a copper calorimeter of mass 66 gm containing 50 gm of water at 20 0C. If the final steady temperature of the calorimeter and its contents is 27.5 0C. Calculate the temperature of flame. (Scopper = 0.4 J/gm0C) [ Ans: 323 0C ]
8. A calorimeter was filled with 50 gm of water at 15 0C. A copper ball of mass 40 gm and temperature 100 0C is dropped into the calorimeter. The final temperature is 20 0C. What would be the final temperature, if instead of copper ball, a silver ball of same mass and temperature were dropped to the calorimeter? ( specific heat capacity of copper, silver and water are 400 J/KgK, 230 J/KgK and 4200 J/KgK respectively) [ Ans: 17.9 0C ]
9. A copper pot with mass 0.5 Kg contains 0.170 Kg of water at a temperature of 20 0C. A 0.250 Kg block of iron at 85 0C is dropped into the pot. Find the final temperature assuming no heat loss to the surroundings? ( specific heat capacity of copper, water and iron are 390 J/KgK, 4190 J/KgK and 470 J/KgK respectively) [ Ans: 27.5 0C ]
10. Two identical calorimeters are each of heat capacity 12 J/K, one contains 8 x 10-5 m3 of water and takes 150 sec to cool from 325 K to 320 K and the other contains an equal volume of an unknown liquid which takes 50 sec to cool over the same range of temperature if the density of liquid is 800 Kgm-3. What is the average specific heat capacity of liquid over the temperature range? ( density of water = 1000 Kgm-3, specific heat capacity of water = 4200 JKg-1K-1 ) [ Ans: 1625 JKg-1K-1]
11. A substance takes 3 min in cooling from 50 0C to 45 0C and takes 5 min in cooling from 45 0C to 40 0C. What is the temperature of the surroundings? How much time will it take to cool this substance from 40 0C to 35 0C? [ Ans: 35 0C, 15 min]
12. The temperature of body falls from 40 0C to 36 0C in 5 minutes. Find the time taken for the temperature of the body to become 32 0C. The temperature of surrounding is 16 0C. [ Ans: 6.1 minutes]
13. A copper calorimeter weighing 53.2 gm is first filled with water then with a liquid. Time taken to cool from 40 0C to 32 0C in the two cases is 4 min and 3 min respectively. The mass of water is 25 gm and that of liquid is 30 gm. Calculate the specific heat capacity of the liquid? ( specific heat capacity of copper = 0.094 cal/gm0C)[ Ans: 0.58 cal/gm0C]
14. During the flu a 80 Kg man ran a fever of 39 0C instead of the normal body temperature of 37 0C. Assuming the human body is mostly made of water, how much heat is required to raise his temperature by that amount? [ Ans: 67200 J ]
15. A copper sphere of mass m falls from height 90 m. If on reaching the ground 75 % of energy is converted into heat, calculate the rise in temperature of sphere. ( sp heat capacity of copper = 0.1 cal/gm0C) [ Ans: 1.60 0C]
16. In a physics lab experiment a student immersed 200 coins (each having mass of 3 gm) in boiling water. After they reached thermal equilibrium, she fished them out and dropped them into 0.240 kg of water at 20 0C in an insulated container of negligible mass. What was the final temperature of the coin? (sp. heat capacity of coin = 390 J/KgK) [ Ans: 35.07 0C ]
17. A nail driven into a board increases in temperature. If we assume that 60 % of the kinetic energy delivered by a 1.80 Kg hammer with a speed of 7.80 m/s is transformed into heat that flows into the nail and does not flow out, what is the temperature increase in 8.00 gm aluminum nail after it is struck ten times? ( specific heat capacity of aluminum = 910 J/KgK) [ Ans: 45.12 0C]
18. The specific gravity of one liquid is 0.7 and that of another liquid is 0.4. Thermal capacity of 4 litres of first liquid and that of 3 litres of second liquid are equal. Calculate the ratio of specific heat capacities of liquids? [ Ans: 1:1 ]
19. There are three liquids A, B and C having equal masses. Their temperatures are respectively 14 0C, 24 0C and 40 0C. When A and B are mixed, the temperature of the mixture becomes 20 0C; when B and C are mixed, the temperature of the mixture becomes 34 0C. What should be the temperature of the mixture when all the liquids are mixed? [ Ans: 30 0C]
Change of Phases (States)
1. Determine the amount of heat required to convert 1 Kg of ice at -10 0C to steam at 100 0C? ( specific heat capacity of ice = 2100 J/Kg0C, specific latent heat of ice = 3.36 x 105 J/Kg and specific latent heat of steam = 2.26 x 106 J/Kg) [Ans: 30.37 x 105 Joules]
2. Calculate the heat required to convert 10 gm of ice at -10 0C to steam at 100 0C? (specific heat capacity of ice = 0.5 cal/g0C, specific latent heat of ice = 80 cal/g and specific latent heat of steam = 540 cal/g) [Ans: 30450 J]
3. What is the result of mixing 20 gm of water at 90 0C with 10 gm of ice at -10 0C? (sp. Heat of ice = 0.5 cal/gm0C, latent heat of fusion of ice = 80 cal/gm) [ Ans: 31.7 0C ]
4. Find the result of mixing 10 gm of ice at -8 0C with 10 gm of water at 12 0C? (sp. Heat of ice = 0.5 cal/gm0C, latent heat of fusion of ice = 80 cal/gm) [ Ans: final temperature of mixture is 0 0C and 1 gm of ice is melted ]
5. What is the result of mixing 100 gm of ice at 0 0C and 100 gm of water at 100 0C? (specific latent heat of fusion of ice = 3.36 x 105 J/Kg) [Ans: 10 0C]
6. 10 gm of steam at 100 0C is passed into a mixture 100 gm of water and 5 gm of ice at 0 0C. Find the resulting temperature of the mixture? [ Ans: 52.2 0C ]
7. Determine the final result when 400 gm of water and 100 gm of ice at 0 0C ate in copper calorimeter of mass 500 gm into which is 10 gm of steam at 100 0C is passed? (Specific heat of copper = 400 J/KgK, specific latent heat of ice = 3.36 x 105 J/Kg and specific latent heat of steam = 2.26 x 106 J/Kg) [ Ans: 80.24 gm of ice melts, final mass of water = 490.24 gm and final temperature of mixture = 0 0C]
8. What is the result of mixing 100 gm of ice at 0 0C into 100 gm of water at 20 0C in an iron vessel of mass 100 gm?(Siron = 0.112 cal/gm0C)[Ans: ice melted 27.8 gm and final temp. 0 0C]
9. What mass of water must evaporate from the surface of 80 Kg human body to cool it by 1 0C. (specific heat capacity of human body is 0.1 cal/gmK and latent heat of vaporization of water at the body temperature is 577 cal/gm) [ Ans: 13.865 gm ]
10. 50 gm of ice at -6 0C is dropped into water at 0 0C. How many grams of water freeze? (Sice = 2000 J/KgK and Lf = 3.36 x 105 JKg-1) [ Ans: 1.786 gm]
11. Evaporation and perspiration is an important mechanism for temperature control of warm-blooded animals. What mass of water must evaporate from the surface of an 80 Kg human body to cool it by 1 0C? The specific heat capacity of human body is approximately 0.1 cal/gm0C and latent heat of vaporization of water at the body temperature is 577 cal/gm. [ Ans: 0.0139 Kg]
12. How will you divide one kg of water at 5 0C into two parts so that when one part is converted into ice, the heat rejected can convert the other part into steam? (Lf = 80 Cal/gm and Lv = 540 cal/gm) [Ans: 882 gm and 118 gm]
13. From what height a block of ice is dropped in order that it may completely melt. It is assumed that 20 % of energy of fall is retained by ice? (Lf = 80 cal/gm) [Ans: 168000 m]
14. From what height must a block of ice be dropped in order that it may completely melt? It is assumed that all of energy of fall is retained by ice. [ Ans: 34300 m]
15. A lead bullet strikes with a velocity of 500 ms-1 and the bullet falls dead. Calculate the rise in temperature of the bullet assuming that 40 % of the heat produced is used in heating the bullet? (Slead = 0.03 cal/gm0C)
16. 50 gm ice at 0 0C is added to 200 gm of water initially at 70 0C in a vacuum flask. When this ice has been melted and the temperature of flask and its contents is 40 0C. When a further 80 gm of ice has been added and has all melted, the temperature of whole becomes 10 0C. Calculate the specific latent heat of fusion of ice, neglecting any loss of heat to the surrounding. [Ans: 90 cal/gm]
17. One gm of ice at 0 0C contracts in volume by 0.091 cm3 on melting. 9 gm of metal is heated to 200 0C and dropped into an ice calorimeter. The decrease in volume is found to be 0.182 cm3. Calculate the specific heat of metal? [Ans: 0.09 cal/gm0C]
18. Calculate the amount of steam at 100 0C that passes into 500 gm of water and 100 gm of ice at 0 0C contained in a copper calorimeter of mass 200 gm so that the final temperature of mixture is raised to 10 0C? (Swater = 4200 J/KgK, Scopper = 100 J/KgK, Lf = 3.36 x 105 J/Kg and Lv = 2.27 x 106 J/Kg) [Ans: 22.5 gm]
19. In an effort to stay awake for an all-night study session, a student makes a cup of coffee by first placing a 200-W electric immersion heater in 0.320 Kg of water (a) How much heat must be added to the water to raise its temperature from 20.0 0C to 80.0 0C? (b) How much time is required? Assume that all of the heater’s power goes into heating the water. [Ans: 80640 J and 403.2 sec]
1. Determine the amount of heat required to convert 1 Kg of ice at -10 0C to steam at 100 0C? ( specific heat capacity of ice = 2100 J/Kg0C, specific latent heat of ice = 3.36 x 105 J/Kg and specific latent heat of steam = 2.26 x 106 J/Kg) [Ans: 30.37 x 105 Joules]
2. Calculate the heat required to convert 10 gm of ice at -10 0C to steam at 100 0C? (specific heat capacity of ice = 0.5 cal/g0C, specific latent heat of ice = 80 cal/g and specific latent heat of steam = 540 cal/g) [Ans: 30450 J]
3. What is the result of mixing 20 gm of water at 90 0C with 10 gm of ice at -10 0C? (sp. Heat of ice = 0.5 cal/gm0C, latent heat of fusion of ice = 80 cal/gm) [ Ans: 31.7 0C ]
4. Find the result of mixing 10 gm of ice at -8 0C with 10 gm of water at 12 0C? (sp. Heat of ice = 0.5 cal/gm0C, latent heat of fusion of ice = 80 cal/gm) [ Ans: final temperature of mixture is 0 0C and 1 gm of ice is melted ]
5. What is the result of mixing 100 gm of ice at 0 0C and 100 gm of water at 100 0C? (specific latent heat of fusion of ice = 3.36 x 105 J/Kg) [Ans: 10 0C]
6. 10 gm of steam at 100 0C is passed into a mixture 100 gm of water and 5 gm of ice at 0 0C. Find the resulting temperature of the mixture? [ Ans: 52.2 0C ]
7. Determine the final result when 400 gm of water and 100 gm of ice at 0 0C ate in copper calorimeter of mass 500 gm into which is 10 gm of steam at 100 0C is passed? (Specific heat of copper = 400 J/KgK, specific latent heat of ice = 3.36 x 105 J/Kg and specific latent heat of steam = 2.26 x 106 J/Kg) [ Ans: 80.24 gm of ice melts, final mass of water = 490.24 gm and final temperature of mixture = 0 0C]
8. What is the result of mixing 100 gm of ice at 0 0C into 100 gm of water at 20 0C in an iron vessel of mass 100 gm?(Siron = 0.112 cal/gm0C)[Ans: ice melted 27.8 gm and final temp. 0 0C]
9. What mass of water must evaporate from the surface of 80 Kg human body to cool it by 1 0C. (specific heat capacity of human body is 0.1 cal/gmK and latent heat of vaporization of water at the body temperature is 577 cal/gm) [ Ans: 13.865 gm ]
10. 50 gm of ice at -6 0C is dropped into water at 0 0C. How many grams of water freeze? (Sice = 2000 J/KgK and Lf = 3.36 x 105 JKg-1) [ Ans: 1.786 gm]
11. Evaporation and perspiration is an important mechanism for temperature control of warm-blooded animals. What mass of water must evaporate from the surface of an 80 Kg human body to cool it by 1 0C? The specific heat capacity of human body is approximately 0.1 cal/gm0C and latent heat of vaporization of water at the body temperature is 577 cal/gm. [ Ans: 0.0139 Kg]
12. How will you divide one kg of water at 5 0C into two parts so that when one part is converted into ice, the heat rejected can convert the other part into steam? (Lf = 80 Cal/gm and Lv = 540 cal/gm) [Ans: 882 gm and 118 gm]
13. From what height a block of ice is dropped in order that it may completely melt. It is assumed that 20 % of energy of fall is retained by ice? (Lf = 80 cal/gm) [Ans: 168000 m]
14. From what height must a block of ice be dropped in order that it may completely melt? It is assumed that all of energy of fall is retained by ice. [ Ans: 34300 m]
15. A lead bullet strikes with a velocity of 500 ms-1 and the bullet falls dead. Calculate the rise in temperature of the bullet assuming that 40 % of the heat produced is used in heating the bullet? (Slead = 0.03 cal/gm0C)
16. 50 gm ice at 0 0C is added to 200 gm of water initially at 70 0C in a vacuum flask. When this ice has been melted and the temperature of flask and its contents is 40 0C. When a further 80 gm of ice has been added and has all melted, the temperature of whole becomes 10 0C. Calculate the specific latent heat of fusion of ice, neglecting any loss of heat to the surrounding. [Ans: 90 cal/gm]
17. One gm of ice at 0 0C contracts in volume by 0.091 cm3 on melting. 9 gm of metal is heated to 200 0C and dropped into an ice calorimeter. The decrease in volume is found to be 0.182 cm3. Calculate the specific heat of metal? [Ans: 0.09 cal/gm0C]
18. Calculate the amount of steam at 100 0C that passes into 500 gm of water and 100 gm of ice at 0 0C contained in a copper calorimeter of mass 200 gm so that the final temperature of mixture is raised to 10 0C? (Swater = 4200 J/KgK, Scopper = 100 J/KgK, Lf = 3.36 x 105 J/Kg and Lv = 2.27 x 106 J/Kg) [Ans: 22.5 gm]
19. In an effort to stay awake for an all-night study session, a student makes a cup of coffee by first placing a 200-W electric immersion heater in 0.320 Kg of water (a) How much heat must be added to the water to raise its temperature from 20.0 0C to 80.0 0C? (b) How much time is required? Assume that all of the heater’s power goes into heating the water. [Ans: 80640 J and 403.2 sec]
Thermal properties of matter (Equation of state and Kinetic theory of gases)
1. Calculate the rms speed at 0 0C of (i) hydrogen molecules and (ii) oxygen molecules, assuming one mole of a gas occupies a volume of 2 x 10-2 m3 at 0 0C and 105 Nm-2 pressures. (Relative molecular mass of hydrogen and oxygen = 2 and 32 respectively) [Ans: 1732 m/s, 433 m/s]
2. Assuming helium molecules have a root means square speed of 900 m/s at 27 0C and 105 Nm-2 pressures, calculate the rms speed at (i) 127 0C and 105 Nm-2 pressures, (ii) 27 0C and 2 x 105 Nm-2 pressures? [Ans: 1039 m/s, 900m/s]
3. (a) What is the average translational kinetic energy of a molecule of an ideal gas at 27 0C? (b) What is the total random translational kinetic energy of the molecules in one mole of this gas? (c) What is the root mean square speed of oxygen molecules at this temperature? [Ans: 6.21 x 10-21 J, 3740 J and 484 m/s]
4. At what temperature will the average speed of oxygen molecules will be sufficient so as to escape from the earth? Escape velocity from the surface of earth is 11.0 km/s, mass of one oxygen molecule is 5.34 x 10-26 Kg and k = 1.38 x 10-23 J/Kg. [Ans: 1.56 x 105 K ]
5. At what temperature is the root mean square speed of nitrogen molecules equal to the root mean square speed of hydrogen molecules at 20.0 0C? [Ans: 3800 0C]
6. By what factor will the rms speed of particular gas molecules increases if the temperature is increased from 100 0C to 200 0C? [Ans: 1.12 times]
7. The volume of an air bubble becomes 11 times on reaching the surface of water from the bottom of a lake. If the height of mercury in the barometer be 75 cm, then calculate the depth of the lake. Density of the water in the lake is 1.02 x 103 Kgm-3. [Ans: 100 m]
8. Two bulbs of equal volume are joined by a narrow tube and are filled with a gas at STP. When one bulb is kept in melting ice and the other in boiling water, calculate the new pressure of the gas? [Ans: 877.65 mm of Hg]
9. Two glass bulbs of equal volume are joined by a narrow tube and are filled with a gas at STP. When one is kept in melting ice and the other is placed in hot bath, the new pressure is 877.6 mm of Hg. Calculate the temperature of hot bath? [Ans: 373 K]
10. A cylindrical tank has a tight fitting piston that allows the volume of the tank to be changed. The tank originally contains 0.110 m3 of the air at pressure of 3.40 atm. The piston is slowly pulled out until the volume of gas is increased to 0.390 m3. If the temperature remains constant, what is the final value of the pressure? [Ans: 97025.64 Pa]
11. Air is filled at 60 0C in a vessel of open mouth. Up to what temperature should the vessel be heated so that (1/4)th part of air may escape? [Ans: 171 0C]
12. Find the rms speed of nitrogen at NTP. Density of N2 = 1.29 Kgm-3 at NTP. [Ans: 484.65 m/s]
13. Helium gas occupies a volume of 0.04 m3 at a pressure of 2 x 105 N/m2 and temperature 300 K. Calculate mass of helium and root mean square speed of its molecules.(relative molecular mass of helium = 4, molar gas constant = 8.3 J/mol K) [Ans: 0.0129 Kg, 1366.57 m/s]
14. A cylinder gas has a mass of 10 Kg and pressure of 8 atmospheres at 27 0C. When some gas is used in cold room at -3 0C, the gas remaining in the cylinder at this temperature has a pressure of 6.4 atmospheres. Calculate the mass of gas used? [Ans: 1.1 Kg]
15. Calculate the pressure in mm of Hg exerted by hydrogen gas if the no. of molecules per cm3 is 6.80 x 1015 and rms speed of the molecules is 1.90 x 103 m/s. (Avogadro’s constant = 6.023 x 1023 mol-1, relative molecular mass of hydrogen = 2.02) [Ans: 0.20183 mm of Hg]
16. Air at 273 K and 1.01 x 105 Nm-2 pressure contains 2.7 x 1025 molecules per cubic meter. How many molecules per cubic meter will there be at a place where (a) the temperature is 223 K and pressure 1.33 x 10-4 Nm-2? (b) the temperature is 223 K and pressure 1.33 x 104 Nm-2? [Ans: (a) 4.35 x 1016 per m3 (b) 4.35 x 1024 molecules/m3]
17. Taking the density of nitrogen at STP to be 1.251 Kgm-3, find the root mean square speed of nitrogen molecules at 127 0C? [Ans: 596.6 m/s]
18. Two containers of volume 4 V and V are connected by a capillary tube. Initially both are at 273 K and contain a gas at pressure 1.01 x 105 Nm-2. The larger is now warmed to 350 K and small is cooled to 250 K. Calculate the final pressure of the system? [Ans: 1.18 x 105 Nm-2]
19. Air may be taken to consist of 80 % of nitrogen molecules and 20 % oxygen molecules of relative molecular masses 28 and 32 respectively. Calculate (a) the ratio of root mean square speed of nitrogen molecules to that of oxygen molecules in air. (b) the ratio of partial pressures of nitrogen and oxygen molecules in air, and (c) the ratio of root mean square speed of nitrogen molecules in air at 10 0C to that at 100 0C? [Ans: 1.07, 4:1 and 0.87:1]
20. Dry air at 15 0C and a pressure of 1 atmosphere consists of 75.5 % of nitrogen and 23.2 % of oxygen by masses. Partial pressures exerted by nitrogen and oxygen are 0.719 x 105 Nm-2 and 0.212 x 105 Nm-2 respectively. Calculate root mean square speeds of nitrogen and oxygen molecules. ( density of air at the given conditions is 1.225 Kgm-3 ) [Ans: 482.8 m/s and 473 m/s]
21. From the kinetic theory of gases deduce a value for the root mean square speed of thermal agitation of the molecules of helium in a vessel at 0 0C. (Density of helium at STP = 0.1785 Kgm-3). If total translational KE of all the molecules of helium in the vessel is 5 x 10-6 J, what is the temperature in another vessel which contains twice the mass of helium and in which the total KE is 10-5 J? [Ans: 1304.8 m/s, 273 K]
22. A 20 L tank contains 0.225 Kg of helium at 18 0C. The molar mass of helium is 4 gm/mol. (a) how many moles of helium are in the tank? (b) What is the pressure in the tank in Pascal’s and atmospheres? [Ans: 56.2 mol, 67.2 atm]
23. A litre flask contains hydrogen at a pressure of 10-2 mm of Hg and a temperature of 27 0C. Calculate (i) rms speed of hydrogen molecules at 27 0C. (ii) Number of molecules in the flask. (density of hydrogen at STP = 0.09 Kgm-3, Avogadro’s constant = 6.023 x 1023 mol-1) [Ans: 1923.43 m/s, 3.22 x 1017]
24. A closed container of volume 0.02 m3 contains a mixture of neon and argon gases at 27 0C and 105 Nm-2 pressures. The total mass of mixture is 28 gm. If the gram molecular weights of neon and argon are 20 and 40 respectively, find the masses of the individual gases in the container, assuming them to be ideal.( R = 8.314 Jmol-1K-1) [Ans: mAr = 24 gm, mNe = 4 gm]
25. An automobile tyre is filled to a gauge pressure of 200 KPa at 10 0C. After driving 100 Km, the temperature within the tyre rises to 40 0C, what is the pressure within the tyre now? [Ans: 232 KPa]
26. An air bubble of volume 1 cm3 rises from bottom of lake 40 m deep at a temperature 12 0C. To what volume does it grow when it reaches the surface which is at temperature 35 0C? (1atm = 1.01 x 105 Pa) [Ans: 5.36 x 10-6 m3]
1. Calculate the rms speed at 0 0C of (i) hydrogen molecules and (ii) oxygen molecules, assuming one mole of a gas occupies a volume of 2 x 10-2 m3 at 0 0C and 105 Nm-2 pressures. (Relative molecular mass of hydrogen and oxygen = 2 and 32 respectively) [Ans: 1732 m/s, 433 m/s]
2. Assuming helium molecules have a root means square speed of 900 m/s at 27 0C and 105 Nm-2 pressures, calculate the rms speed at (i) 127 0C and 105 Nm-2 pressures, (ii) 27 0C and 2 x 105 Nm-2 pressures? [Ans: 1039 m/s, 900m/s]
3. (a) What is the average translational kinetic energy of a molecule of an ideal gas at 27 0C? (b) What is the total random translational kinetic energy of the molecules in one mole of this gas? (c) What is the root mean square speed of oxygen molecules at this temperature? [Ans: 6.21 x 10-21 J, 3740 J and 484 m/s]
4. At what temperature will the average speed of oxygen molecules will be sufficient so as to escape from the earth? Escape velocity from the surface of earth is 11.0 km/s, mass of one oxygen molecule is 5.34 x 10-26 Kg and k = 1.38 x 10-23 J/Kg. [Ans: 1.56 x 105 K ]
5. At what temperature is the root mean square speed of nitrogen molecules equal to the root mean square speed of hydrogen molecules at 20.0 0C? [Ans: 3800 0C]
6. By what factor will the rms speed of particular gas molecules increases if the temperature is increased from 100 0C to 200 0C? [Ans: 1.12 times]
7. The volume of an air bubble becomes 11 times on reaching the surface of water from the bottom of a lake. If the height of mercury in the barometer be 75 cm, then calculate the depth of the lake. Density of the water in the lake is 1.02 x 103 Kgm-3. [Ans: 100 m]
8. Two bulbs of equal volume are joined by a narrow tube and are filled with a gas at STP. When one bulb is kept in melting ice and the other in boiling water, calculate the new pressure of the gas? [Ans: 877.65 mm of Hg]
9. Two glass bulbs of equal volume are joined by a narrow tube and are filled with a gas at STP. When one is kept in melting ice and the other is placed in hot bath, the new pressure is 877.6 mm of Hg. Calculate the temperature of hot bath? [Ans: 373 K]
10. A cylindrical tank has a tight fitting piston that allows the volume of the tank to be changed. The tank originally contains 0.110 m3 of the air at pressure of 3.40 atm. The piston is slowly pulled out until the volume of gas is increased to 0.390 m3. If the temperature remains constant, what is the final value of the pressure? [Ans: 97025.64 Pa]
11. Air is filled at 60 0C in a vessel of open mouth. Up to what temperature should the vessel be heated so that (1/4)th part of air may escape? [Ans: 171 0C]
12. Find the rms speed of nitrogen at NTP. Density of N2 = 1.29 Kgm-3 at NTP. [Ans: 484.65 m/s]
13. Helium gas occupies a volume of 0.04 m3 at a pressure of 2 x 105 N/m2 and temperature 300 K. Calculate mass of helium and root mean square speed of its molecules.(relative molecular mass of helium = 4, molar gas constant = 8.3 J/mol K) [Ans: 0.0129 Kg, 1366.57 m/s]
14. A cylinder gas has a mass of 10 Kg and pressure of 8 atmospheres at 27 0C. When some gas is used in cold room at -3 0C, the gas remaining in the cylinder at this temperature has a pressure of 6.4 atmospheres. Calculate the mass of gas used? [Ans: 1.1 Kg]
15. Calculate the pressure in mm of Hg exerted by hydrogen gas if the no. of molecules per cm3 is 6.80 x 1015 and rms speed of the molecules is 1.90 x 103 m/s. (Avogadro’s constant = 6.023 x 1023 mol-1, relative molecular mass of hydrogen = 2.02) [Ans: 0.20183 mm of Hg]
16. Air at 273 K and 1.01 x 105 Nm-2 pressure contains 2.7 x 1025 molecules per cubic meter. How many molecules per cubic meter will there be at a place where (a) the temperature is 223 K and pressure 1.33 x 10-4 Nm-2? (b) the temperature is 223 K and pressure 1.33 x 104 Nm-2? [Ans: (a) 4.35 x 1016 per m3 (b) 4.35 x 1024 molecules/m3]
17. Taking the density of nitrogen at STP to be 1.251 Kgm-3, find the root mean square speed of nitrogen molecules at 127 0C? [Ans: 596.6 m/s]
18. Two containers of volume 4 V and V are connected by a capillary tube. Initially both are at 273 K and contain a gas at pressure 1.01 x 105 Nm-2. The larger is now warmed to 350 K and small is cooled to 250 K. Calculate the final pressure of the system? [Ans: 1.18 x 105 Nm-2]
19. Air may be taken to consist of 80 % of nitrogen molecules and 20 % oxygen molecules of relative molecular masses 28 and 32 respectively. Calculate (a) the ratio of root mean square speed of nitrogen molecules to that of oxygen molecules in air. (b) the ratio of partial pressures of nitrogen and oxygen molecules in air, and (c) the ratio of root mean square speed of nitrogen molecules in air at 10 0C to that at 100 0C? [Ans: 1.07, 4:1 and 0.87:1]
20. Dry air at 15 0C and a pressure of 1 atmosphere consists of 75.5 % of nitrogen and 23.2 % of oxygen by masses. Partial pressures exerted by nitrogen and oxygen are 0.719 x 105 Nm-2 and 0.212 x 105 Nm-2 respectively. Calculate root mean square speeds of nitrogen and oxygen molecules. ( density of air at the given conditions is 1.225 Kgm-3 ) [Ans: 482.8 m/s and 473 m/s]
21. From the kinetic theory of gases deduce a value for the root mean square speed of thermal agitation of the molecules of helium in a vessel at 0 0C. (Density of helium at STP = 0.1785 Kgm-3). If total translational KE of all the molecules of helium in the vessel is 5 x 10-6 J, what is the temperature in another vessel which contains twice the mass of helium and in which the total KE is 10-5 J? [Ans: 1304.8 m/s, 273 K]
22. A 20 L tank contains 0.225 Kg of helium at 18 0C. The molar mass of helium is 4 gm/mol. (a) how many moles of helium are in the tank? (b) What is the pressure in the tank in Pascal’s and atmospheres? [Ans: 56.2 mol, 67.2 atm]
23. A litre flask contains hydrogen at a pressure of 10-2 mm of Hg and a temperature of 27 0C. Calculate (i) rms speed of hydrogen molecules at 27 0C. (ii) Number of molecules in the flask. (density of hydrogen at STP = 0.09 Kgm-3, Avogadro’s constant = 6.023 x 1023 mol-1) [Ans: 1923.43 m/s, 3.22 x 1017]
24. A closed container of volume 0.02 m3 contains a mixture of neon and argon gases at 27 0C and 105 Nm-2 pressures. The total mass of mixture is 28 gm. If the gram molecular weights of neon and argon are 20 and 40 respectively, find the masses of the individual gases in the container, assuming them to be ideal.( R = 8.314 Jmol-1K-1) [Ans: mAr = 24 gm, mNe = 4 gm]
25. An automobile tyre is filled to a gauge pressure of 200 KPa at 10 0C. After driving 100 Km, the temperature within the tyre rises to 40 0C, what is the pressure within the tyre now? [Ans: 232 KPa]
26. An air bubble of volume 1 cm3 rises from bottom of lake 40 m deep at a temperature 12 0C. To what volume does it grow when it reaches the surface which is at temperature 35 0C? (1atm = 1.01 x 105 Pa) [Ans: 5.36 x 10-6 m3]
First law of Thermodynamics
1. A system absorbs 300 cal and at the same time 400 J of work is done on it. Find change in internal energy system. [Ans: 1660 J]
2. One gm of water becomes 1601 cc of steam when boiled at a pressure of 1 atmosphere. The heat of vaporization at this temperature is 540 cal/gm. Compute the external work done and increase in internal energy? [Ans: 499.7 cal, 40.3 cal]
3. One mole of a gas at 400 K expands isothermally until its volume doubles. Calculate the amount of work done? [Ans: 2.3 x 103 J]
4. From the values of Cv and CP calculate (i) heat needed to raise the temperature of 8 gm of hydrogen from 10 0C to 15 0C at constant pressure, (ii) the increase in internal energy of the gas and (iii) the external work done? (molar mass of hydrogen = 2 gm, Cv = 20.5 J mol-1 K-1 and CP = 28.8 J mol-1 K-1) [Ans: 576 J, 410 J, 166 J]
5. Five moles of an ideal gas are kept at constant temperature of 53 0C while pressure of gas is increased from 1.00 atm to 3.00 atm. Calculate work done by gas. [Ans: -14881 J]
6. 16 gm of oxygen having volume 0.02 m-3 at a temperature of 27 0C and a pressure of 2 x 105 Nm-2 is heated at constant pressure until its volume increases to 0.03 m3. Calculate the external work done and increase in internal energy of the gas if its molar heat capacity at constant volume is 0.8 J mol-1 K-1 and molar mass of oxygen is 32. [Ans: 2 x 103 J, 60 J]
7. Gas in a cylinder initially at a temperature of 10 0C and pressure of 1.01 x 105 Nm-2 is to be compressed adiabatically to one eighth of its volume. Find final pressure and temperature. (given γ = 1.40 ) [Ans: 18.5 x 105 Nm-2, 560.16 K]
8. A mass of air occupying initially volume 2 x 10-3 m3 at a pressure of 760 mm of Hg and a temperature of 20 0C is expanded adiabatically and reversibly to twice its volume, and then compressed isothermally and reversibly to a volume of 3 x 10-3 m3. Find the final pressure assuming the ratio of specific heat capacities of air to be 1.4? [Ans: 384 mm of Hg]
9. A gasoline engine takes in air at 25 0C and one atmospheric pressure and compresses adiabatically to one-tenth of its original volume. Find the final temperature and pressure. ( γ = 1.4 ) [Ans: 784.5 K, 25.11 atmospheres]
10. The density of a gas is 1.775 Kgm-3 at 27 0C and 105 Nm-2 pressures. If the specific heat capacity at constant pressure is 846 J Kg-1 K-1. Find the ratio of specific heat capacity at constant pressure to that at constant volume? [Ans: 1.29]
11. A gas is slowly compressed at constant temperature of 50 0C to one half of its initial volume. In this process, 80 cal of heat was given. How much work was done and what was the change in internal energy of the gas? Assume one mole of gas. [Ans: 1858.26 J, 2196.49 J]
12. A litre of air initially at 20 0C and at 760 mm of Hg pressure is heated at constant pressure until its volume is doubled. Find the final temperature and external work done by the gas in expanding and the quantity of heat supplied? (specific heat capacity at constant volume = 714 J / Kg K) [Ans: 586 K, 101.3 J, 352.8 J]
13. An ideal gas initially at 4 atmosphere and 300 K is permitted to expand adiabatically twice its initial volume. Find the final pressure and temperature if the gas is (a) monatomic and (ii) diatomic with CV = 5/2 R. [Ans: (a) 1.257 atm; 189 K (b) 1.52 atm; 227.35 K]
14. An ideal gas at 17 0C has a pressure of 760 mm of Hg, and is compressed (i) isothermally and (ii) adiabatically until its volume is halved, in each case reversibly. Calculate in each cases the final pressure and temperature of the gas, assuming cp = 2100 J/KgK and cv = 1500 J/KgK. [Ans: (i) 1520 mm of Hg, 290 K (ii) 2005.6 mm of Hg, 382.66 K]
15. Gas in a cylinder, initially at a temperature of 17 0C and a pressure of 1.01 x 105 Nm-2, is to be compressed to one-eighth of its volume. What would be the difference between the final pressures if the compression were done (a) isothermally and (b) adiabatically? What would be the final temperature on later case? Ratio of molar heat capacities = 1.4 [Ans: 1.048 x 106 Pa, 666 K]
16. Five moles of an ideal monatomic gas with an initial temperature of 127 0C expands and in this process, absorb 1200 J of heat and do 2100 J of work. What is the final temperature of the gas? [Ans: 385.6 K]
17. A quantity of oxygen is compressed isothermally until its pressure is doubled. It is then allowed to expand adiabatically until its original volume is recorded find the final pressure in terms of the initial pressure.(the ratio of molar heat capacities of oxygen is to be taken as 1.40) [Ans: 0.76 P]
18. Given that the volume of a gas at STP is 2.24 x 10-2 m3mol-1 and that standard pressure is 1.01 x 105 N/m2, calculate value for the molar gas constant R and use it to find the difference between the quantities of heat required to raise the temperature of 0.01 Kg of oxygen from 0 0C to 10 0C when (a) the pressure, (b) the volume of the gas is kept constant. (Relative molecular mass of oxygen = 32) [Ans: 8.3 J mol-1 K-1, r = 258.97 J/KgK, 25.89 J]
19. A cylinder containing 19 Kg of compressed air at a pressure 9.5 times of the atmosphere is kept in a store at 7 0C. When it is moved to a workshop where the temperature is 27 0C a safety valve on the cylinder operates, releasing some of the air. If the valve allows air to escape when its pressure exceeds 10 times that of the atmosphere, calculate the mass of air that escapes? [Ans: 0.33 Kg]
20. An ideal gas having initial pressure P, volume V and temperature T is allowed to expand adiabatically until its volume becomes 5.66 V while its temperature falls to T/2. (i) What is the value of γ for the gas? (ii) Obtain the work done by the gas during expansion as function of initial pressure P and volume V? [Ans: 1.4, 1.25 PV]
21. A given mass of air, initially at a temperature of 27 0C is compressed (i) slowly and (ii) suddenly, to one third of its original volume. Calculate the change in temperature in both cases. (γ for air = 1.3) [Ans: 0 K and 165.6 K]
22. A copper ball of mass 0.100 Kg falls on earth from a height of 10 m and bounces to a height of 1.0 m. If all the mechanical energy dissipated remains in the ball as heat and specific heat of copper is 0.1 kilocal/Kg0C, then find (i) workdone on the ball (ii) change in internal energy of ball and (iii) rise in temperature of the ball after striking. [Ans: -9 J, 9 J, 0.214 0C]
1. A system absorbs 300 cal and at the same time 400 J of work is done on it. Find change in internal energy system. [Ans: 1660 J]
2. One gm of water becomes 1601 cc of steam when boiled at a pressure of 1 atmosphere. The heat of vaporization at this temperature is 540 cal/gm. Compute the external work done and increase in internal energy? [Ans: 499.7 cal, 40.3 cal]
3. One mole of a gas at 400 K expands isothermally until its volume doubles. Calculate the amount of work done? [Ans: 2.3 x 103 J]
4. From the values of Cv and CP calculate (i) heat needed to raise the temperature of 8 gm of hydrogen from 10 0C to 15 0C at constant pressure, (ii) the increase in internal energy of the gas and (iii) the external work done? (molar mass of hydrogen = 2 gm, Cv = 20.5 J mol-1 K-1 and CP = 28.8 J mol-1 K-1) [Ans: 576 J, 410 J, 166 J]
5. Five moles of an ideal gas are kept at constant temperature of 53 0C while pressure of gas is increased from 1.00 atm to 3.00 atm. Calculate work done by gas. [Ans: -14881 J]
6. 16 gm of oxygen having volume 0.02 m-3 at a temperature of 27 0C and a pressure of 2 x 105 Nm-2 is heated at constant pressure until its volume increases to 0.03 m3. Calculate the external work done and increase in internal energy of the gas if its molar heat capacity at constant volume is 0.8 J mol-1 K-1 and molar mass of oxygen is 32. [Ans: 2 x 103 J, 60 J]
7. Gas in a cylinder initially at a temperature of 10 0C and pressure of 1.01 x 105 Nm-2 is to be compressed adiabatically to one eighth of its volume. Find final pressure and temperature. (given γ = 1.40 ) [Ans: 18.5 x 105 Nm-2, 560.16 K]
8. A mass of air occupying initially volume 2 x 10-3 m3 at a pressure of 760 mm of Hg and a temperature of 20 0C is expanded adiabatically and reversibly to twice its volume, and then compressed isothermally and reversibly to a volume of 3 x 10-3 m3. Find the final pressure assuming the ratio of specific heat capacities of air to be 1.4? [Ans: 384 mm of Hg]
9. A gasoline engine takes in air at 25 0C and one atmospheric pressure and compresses adiabatically to one-tenth of its original volume. Find the final temperature and pressure. ( γ = 1.4 ) [Ans: 784.5 K, 25.11 atmospheres]
10. The density of a gas is 1.775 Kgm-3 at 27 0C and 105 Nm-2 pressures. If the specific heat capacity at constant pressure is 846 J Kg-1 K-1. Find the ratio of specific heat capacity at constant pressure to that at constant volume? [Ans: 1.29]
11. A gas is slowly compressed at constant temperature of 50 0C to one half of its initial volume. In this process, 80 cal of heat was given. How much work was done and what was the change in internal energy of the gas? Assume one mole of gas. [Ans: 1858.26 J, 2196.49 J]
12. A litre of air initially at 20 0C and at 760 mm of Hg pressure is heated at constant pressure until its volume is doubled. Find the final temperature and external work done by the gas in expanding and the quantity of heat supplied? (specific heat capacity at constant volume = 714 J / Kg K) [Ans: 586 K, 101.3 J, 352.8 J]
13. An ideal gas initially at 4 atmosphere and 300 K is permitted to expand adiabatically twice its initial volume. Find the final pressure and temperature if the gas is (a) monatomic and (ii) diatomic with CV = 5/2 R. [Ans: (a) 1.257 atm; 189 K (b) 1.52 atm; 227.35 K]
14. An ideal gas at 17 0C has a pressure of 760 mm of Hg, and is compressed (i) isothermally and (ii) adiabatically until its volume is halved, in each case reversibly. Calculate in each cases the final pressure and temperature of the gas, assuming cp = 2100 J/KgK and cv = 1500 J/KgK. [Ans: (i) 1520 mm of Hg, 290 K (ii) 2005.6 mm of Hg, 382.66 K]
15. Gas in a cylinder, initially at a temperature of 17 0C and a pressure of 1.01 x 105 Nm-2, is to be compressed to one-eighth of its volume. What would be the difference between the final pressures if the compression were done (a) isothermally and (b) adiabatically? What would be the final temperature on later case? Ratio of molar heat capacities = 1.4 [Ans: 1.048 x 106 Pa, 666 K]
16. Five moles of an ideal monatomic gas with an initial temperature of 127 0C expands and in this process, absorb 1200 J of heat and do 2100 J of work. What is the final temperature of the gas? [Ans: 385.6 K]
17. A quantity of oxygen is compressed isothermally until its pressure is doubled. It is then allowed to expand adiabatically until its original volume is recorded find the final pressure in terms of the initial pressure.(the ratio of molar heat capacities of oxygen is to be taken as 1.40) [Ans: 0.76 P]
18. Given that the volume of a gas at STP is 2.24 x 10-2 m3mol-1 and that standard pressure is 1.01 x 105 N/m2, calculate value for the molar gas constant R and use it to find the difference between the quantities of heat required to raise the temperature of 0.01 Kg of oxygen from 0 0C to 10 0C when (a) the pressure, (b) the volume of the gas is kept constant. (Relative molecular mass of oxygen = 32) [Ans: 8.3 J mol-1 K-1, r = 258.97 J/KgK, 25.89 J]
19. A cylinder containing 19 Kg of compressed air at a pressure 9.5 times of the atmosphere is kept in a store at 7 0C. When it is moved to a workshop where the temperature is 27 0C a safety valve on the cylinder operates, releasing some of the air. If the valve allows air to escape when its pressure exceeds 10 times that of the atmosphere, calculate the mass of air that escapes? [Ans: 0.33 Kg]
20. An ideal gas having initial pressure P, volume V and temperature T is allowed to expand adiabatically until its volume becomes 5.66 V while its temperature falls to T/2. (i) What is the value of γ for the gas? (ii) Obtain the work done by the gas during expansion as function of initial pressure P and volume V? [Ans: 1.4, 1.25 PV]
21. A given mass of air, initially at a temperature of 27 0C is compressed (i) slowly and (ii) suddenly, to one third of its original volume. Calculate the change in temperature in both cases. (γ for air = 1.3) [Ans: 0 K and 165.6 K]
22. A copper ball of mass 0.100 Kg falls on earth from a height of 10 m and bounces to a height of 1.0 m. If all the mechanical energy dissipated remains in the ball as heat and specific heat of copper is 0.1 kilocal/Kg0C, then find (i) workdone on the ball (ii) change in internal energy of ball and (iii) rise in temperature of the ball after striking. [Ans: -9 J, 9 J, 0.214 0C]
Second Law of Thermodynamics
1. A Carnot engine absorbs heat from a reservoir at the temperature of 100 0C and rejects heat to a reservoir at a temperature of 0 0C. If the engine absorbs 1000 Joules of heat from the high temperature reservoir find, the heat rejected, work done and the efficiency? [Ans: 731.9 J, 268.1 J, 26.8 %]
2. A Carnot engine has the same efficiency between 100 K and 500K and between T K and 900 K. Calculate the temperature T K of the sink? [Ans: 180 K]
3. A Carnot engine has efficiency 50 % with a sink at 9 0C. By how many degrees should the temperature of source be increased in order to raise the efficiency to 70 %? [Ans: 376 K]
4. A reversible engine converts one sixth of heat input into work. When the temperature of sink is reduced by 62 0C, its efficiency is doubled. Find the temperature of the source and the sink? [372 K, 310 K]
5. A Carnot engine whose low temperature reservoir is at 27 0C has an efficiency of 25 %. In order to increase the efficiency to 50 %, how much the temperature of the high temperature reservoir be increased, if the temperature of low temperature reservoir remains constant? [Ans: ]
6. A petrol engine consumes 5 Kg of petrol per hour. If the power of engine is 20 KW and the calorific value of petrol is 11 x 103 Kcal per Kg. Calculate efficiency of engine? [Ans: 31.15 %]
7. In a petrol engine the rate of production of heat due to combustion of fuel is 7.46 x 105 cal/hr. If the efficiency of engine is 30 %, Calculate the horse power of engine. ( 1 HP = 746 W) [Ans: 0.35 HP]
8. How much heat energy is required to do 10 KWh of work by a petrol engine whose adiabatic compression ratio is 10? (γ = 1.4) [Ans: 1.424 x 107 cal]
9. One kilogram of water at 0 0C is heated to 100 0C. Compute change in entropy? [Ans 1.31 x 103 J/K]
10. A refrigerator has a coefficient of performance 2.10. In each cycle it absorbs 3.40 x 104 J of heat from cold reservoir. (a) how much mechanical energy is required in each cycle to operate refrigerator? (b) during each cycle, how much heat is rejected to the high temperature reservoir? [Ans: 1.619 x 104 J, 5.02 x 104 J]
1. A Carnot engine absorbs heat from a reservoir at the temperature of 100 0C and rejects heat to a reservoir at a temperature of 0 0C. If the engine absorbs 1000 Joules of heat from the high temperature reservoir find, the heat rejected, work done and the efficiency? [Ans: 731.9 J, 268.1 J, 26.8 %]
2. A Carnot engine has the same efficiency between 100 K and 500K and between T K and 900 K. Calculate the temperature T K of the sink? [Ans: 180 K]
3. A Carnot engine has efficiency 50 % with a sink at 9 0C. By how many degrees should the temperature of source be increased in order to raise the efficiency to 70 %? [Ans: 376 K]
4. A reversible engine converts one sixth of heat input into work. When the temperature of sink is reduced by 62 0C, its efficiency is doubled. Find the temperature of the source and the sink? [372 K, 310 K]
5. A Carnot engine whose low temperature reservoir is at 27 0C has an efficiency of 25 %. In order to increase the efficiency to 50 %, how much the temperature of the high temperature reservoir be increased, if the temperature of low temperature reservoir remains constant? [Ans: ]
6. A petrol engine consumes 5 Kg of petrol per hour. If the power of engine is 20 KW and the calorific value of petrol is 11 x 103 Kcal per Kg. Calculate efficiency of engine? [Ans: 31.15 %]
7. In a petrol engine the rate of production of heat due to combustion of fuel is 7.46 x 105 cal/hr. If the efficiency of engine is 30 %, Calculate the horse power of engine. ( 1 HP = 746 W) [Ans: 0.35 HP]
8. How much heat energy is required to do 10 KWh of work by a petrol engine whose adiabatic compression ratio is 10? (γ = 1.4) [Ans: 1.424 x 107 cal]
9. One kilogram of water at 0 0C is heated to 100 0C. Compute change in entropy? [Ans 1.31 x 103 J/K]
10. A refrigerator has a coefficient of performance 2.10. In each cycle it absorbs 3.40 x 104 J of heat from cold reservoir. (a) how much mechanical energy is required in each cycle to operate refrigerator? (b) during each cycle, how much heat is rejected to the high temperature reservoir? [Ans: 1.619 x 104 J, 5.02 x 104 J]