Thermal expansion: short questions and numericals
Written By: Mr. Amrit Panthi ( Lecturer of Physics)
1. Two bodies made up of same material have the same dimension and appearance but one is solid and other is hollow. When they are heated is the overall expansion same?
2. In question no. 1, if equal amount of energy is supplied then what will happen?
3. In question no. 1, if temperature is raised equally by heating then what will happen?
4. Why do solids expand on heating?
5. Why do frozen water pipe often burst?
6. Why is it sometime possible to loosen caps on screw top bottles by deeping into hot water?
7. Explain why the column of mercury in thermometer at first falls and then rises when placed in hot water?
8. Does the coefficient of linear expansion depends on length? Explain.
9. Fishes stay alive in frozen pond in winter explain?
10. Why does a thick glass tumbler crack when hot water is poured into it?
11. Why are glass window possible to be cracked in very cold region?
12. A hole is drilled in a flat metal sheet. What happens to the diameter of a hole as the metal sheet is heated to a higher temperature?
13. It is possible to seal a piece of platinum but not brass or iron wire into a glass tube. Why?
14. Frozen pipe often bursts, will a mercury thermometer bursts if it is brought below the freezing point of mercury?
15. Does the cubical expansivity of liquid depends on the original volume of liquid? Explain.
16. What is the anamolous expansion of water? How is it useful?
17. Define coefficients of cubical expansion, superficial expansion and linear expansion?
18. What do you mean by real and apparent expansion of liquids?
19. What is the effect of temperature on density of liquid?
20. Liquid has only cubical expansion, why?
21. Two identical rectangular strips of copper and steel are pivoted to form a bimetallic strip. What will happen on heating?
22. Why do clock not keep correct time in summer and winter? Why is invar used in making clock pendulum?
23. A clock which has brass pendulum correctly beats at 300C. Will it run faster or slower if the temperature: a) increases and b) decreases?
24. Why in drinking hot water, a thin bottomed glass is used?
25. Define temperature in terms of zeroth law of thermodynamics?
26. Why do solids expand when their temperature is raised?
27. Can an object be hotter than other if they are at same temperature?
28. Iron rims are heated red hot before planted in a cart wheels. Why?
29. Why are small spaces left between successive rails of railway track?
30. Two rectangular strips of brass and steel are pivoted to form a bimetallic strip. What will happen on heating?
31. What is the effect of temperature on the density of liquid?
32. What do you mean by differential expansion? Under what condition it is zero?
33. What type of expansivity does liquids have?
34. Why telephones wires on a pole are taut in winter days and lowered in summer days?
35. A beaker full of water at four degree Celsius. What will happen if the temperature of water a) increases. b) Decreases.
36. Why should the amalgam used in dental fillings have the same average coefficient of expansion as a tooth? What would occur if they were mismatched?
37. Metal knob of door is colder than wooden parts at the same temperature. Why?
38. Fishes stay alive in frozen pond in winter. Why?
Numericals:
1. The density of silver at 00C is 10310 kg/m3 and the coefficient of linear expansion is 0.000019/0C. Calculate the density at 1000C. 10251.56 Kg/m3
2. A copper vessel with a volume exactly 100m3 at a temperature of 150C is filled with glycerin. If the temperature rises to 250C. How much glycerin will spill out? αcopper = 16.7 x 10-6/0C & ϒglycerin = 5.3 x 10-4/0C. 0.48m3
3. A steel tank is completely filled with 2.8m3 of ethanol when both the tank and the ethanol are at a temperature of 320C. When the tank and its contents have cooled to 180C. What additional volume can be put into the tank? (Assume the volume of tank does not change. (ϒ for ethanol = 75x10-5/K. 0.029m3
4. A glass flask of volume 400cm3 is just filled with mercury at 00C. How much mercury overflow when the temperature of the system is raised to 800C? (ϒ for glass = 1.2x10-5/0C and ϒ for mercury = 1.8x10-5/0C) 0.192x10-6m3
5. A glass flask whose volume is exactly 1000 cm3 at 00C is filled full of mercury at this temperature. When flask and mercury are heated to 1000C, 15.2cm3 of mercury overflows. If the cubical expansivity for mercury is 0.0001820C-1. Find the linear expansivity of glass? 10-5 0C-1
6. A bottle has a volume of 100cm3 at 00C and is filled with mercury at 300C. Calculate the mass of mercury filling the bottle, given that the density of mercury at 00C is 13600Kgm-3, its absolute cubical expansivity is 1.8x10-4K-1, and the linear expansivity of glass is 9x10-6K-1. 1.354Kg
7. A piece of steel floats in mercury at 00C with 57.35% of its volume submerged. What percentage of its volume will be submerged when the temperature is raised through 500C? (Relative densities of steel and mercury are 7.8 and 13.6 respectively. Linear expansivity of steel = 12x10-6K-1. Cubical expansivity of mercury = 18x10-5K-1. 57.7%
8. Using the following data determine the temperature at which wood will just sink in benzene? Density of benzene at 00C is 900Kgm-3, density of wood at 00C is 880Kgm-3, cubical expansivity of benzene is 1.2x10-3/K and that of wood is 1.5x10-4/K. 33.0030C
9. In an experiment performed by Dulong and Petit’s method the heights of the cold and hot columns mercury are found to be 99.5 and 101.2 cms respectively. If the temperature of cold of column is 00C. Calculate the temperature of hot column. { ϒ for mercury = 18x10-5K-1.}
10. A glass vessel contains when full 544 gms of mercury at 00C. The mass of mercury which fills it at 1000C is 535.45 gm. calculate the cubical expansivity of glass. ϒHg=18x10-5K-1 2x10-5K-1
11. A copper cylinder is initially at 20.00C. At what temperature will its volume be 0.150% larger than it is at 20.00C? αcopper = 16.7 x 10-6/0C 109.50C
12. The pendulum of a clock is made of brass. If the clock keeps correct time at 150C. How many seconds per day will it loose at 200C? 4s
13. A clock which has a brass pendulum beats seconds correctly when the temperature of the room is 300C. How many seconds does it gains or loose per day when the temperature of the room becomes 100C? αbrass=0.0000180C-1. 16.92s gain
14. A steel wire 8m long and 4mm in diameter is fixed to two rigid supports. Calculate the increase in tension when the temperature falls by 100C. given αsteel=12x10-6C-1 Ysteel=2x1011N/m2 301.6N
15. A steel rod whose length at 00C is 1.42m is heated to 80.00C. The increase in length was found to be 0.135cm. Find the coefficient of linear expansion of steel? 12x10-6/K
16. The length of iron rod is 50cm at 00C and 50.06cm at 1000C. Calculate its length at 500C? 50.03cm
17. An aluminum rod when measured with a steel scale, both being at 250C appears to be 1m long. If the scale is correct at 00C; what will be the length of the rod at 00C? Linear expansivity of steel=12x10-6K-1 and that of aluminum is 26x10-6K-1? 0.99m
18. A brass rod of length 0.40m and steel rod of length 0.60m, both are initially at 00C are heated to 750C. If the increase in lengths is the same for both the rods, calculate linear expansivity of brass. The linear expansivity of steel is 12x10-6 /0C. 18x10-6/0C
19. The length of iron rod is measured by a brass scale. When both of them are at 100C, the measured length is 50cm. what is the length of rod at 400C when measured by the brass scale at 400C? (linear expansivity for brass is 24x10-6K-1and that for iron is 16x10-6K-1. 49.98cm
20. A steel rod when measured with a zinc scale both being at 250C appear to be 1 meter long. If the zinc scale is correct at 00C, what is the actual length of rod at 250C? What will be the length of the rod at 00C? αsteel=12x10-6 0C-1 αzinc=12x10-6 0C-1 1.00065, 1.00035
21. A brass rod and a steel rod differ by 10cm in length at all temperatures. What are their lengths at 00C. αsteel=12x10-6 0C-1 αbrass=18x10-6 0C-1 20cm, 30cm
22. A surveyor’s 300m steel tape is correct at a temperature of 200C. The distance between two points, as measured by this tape on a day when the temperature is 50C is 200m. what is the true distance between the two points? αsteel=12x10-6C-1 199.964m