MCQs

1. A piece of copper wire has a length of 100 cm at 5^oC. Its length at 478 K will be (given: [latex]\alpha = 17\times 10^{-6}[/latex] ^oC^-1)

1. 100. 34 cm
2. 200.34 cm
3. 100.80 cm
4. 101.2 cm

2. Which of the following is correct for solids?

1. [latex]\gamma = \frac{2}{3}\beta[/latex]
2. [latex]\gamma = \frac{3}{2}\beta[/latex]
3. [latex]\gamma = \frac{3}{2}\alpha[/latex]
4. [latex]\gamma = \frac{2}{3}\alpha[/latex]

3. The increase in length of a body of 50 meter length is 2.3 mm when the body is heated from 0^oC to 50^oC. The coefficient of linear expansion of the body is

1. [latex]4.6\times 10^{-4}/^oC[/latex]
2. [latex]4.6\times 10^{-6}/^oC[/latex]
3. [latex]4.6\times 10^{-5}/^oC[/latex]
4. [latex]2.3\times 10^{-5}/^oC[/latex]

4. Lengths of two metal bars ‘A’ and ‘B’ are 8 cm and 12 cm respectively. If they show same difference in lengths at all temperature, their superficial expansivities are in the ratio

1. 2:3
2. 3:2
3. 9:4
4. 4:9

5. A clock has copper pendulum beats seconds correctly when temperature of the room is 30^oC, the time loss or gain per day when temperature falls to 10^oC is ([latex]\alpha = 1.9\times 10^{-5} K^{-1}[/latex]).

1. gain 17.28 s
2. loss 16.43 s
3. loss 4.2 s
4. gain 4.2 s

6. Which material has least value of expansivity?

1. alnico                          
2. invar                       
3. steel                        
4. nickel

7. The ratio of real expansivity to apparent expansivity of a liquid is            

1. < 1                              
2. equal to 1               
3. > 1                          
4. 0

Answers

1.a

2.b

3.c

4.b

5.a

6.b

7.c

CONCEPTUAL PROBLEMS

1. Two metallic rods of the same material but of different length are heated. Smaller rod has circular area of cross – section but larger rod had rectangular cross – section. Will their linear expansivity be the same or different? Give justification of your answer.
2. Why is it sometimes possible to loosen caps on screw top bottles by dipping the cap briefly in hot water?
3. Explain why the possibility of “water taps burst” rise in severe winter.
4. A square brass plate has a large circular hole cut in its centre. If the plate is heated, it will expand. Will the diameter of the hole expand or contract? Explain your answer.
5. Define the coefficient of cubical expansion of a solid and hence write an expression for the variation of its density with temperature.
6. Frozen water pipes often burst. Will an alcohol thermometer break if the temperature drops below the freezing point of alcohol?
7. A hole is drilled in a flat metal sheet. What happens to the diameter of the hole as the metal sheet is heated to higher temperature?
8. Does the cubical expansivity of a liquid depend on its original volume? Explain.
9. Frozen water pipes often burst; will a mercury thermometer break if the temperature of the thermometer is brought below the freezing point of mercury?
10. Does the coefficient of linear expansion depend on length? Justify your answer.
11. Why are glass windows possible to be cracked in very cold region?
12. Two bodies made of the same material have the same external dimension and appearance, but one is solid and the other is hollow. When they are heated, is the overall volume expansion the same or different?
13. Why does a thick glass tumbler crack when boiling water is poured on it?
14. Water level initially falls in a vessel when it is heated. Why?

THEORY BASED PROBLEMS

15. Define coefficients of real and apparent expansion of a liquid and establish a relation between them.
16. Define the coefficients of linear and cubical expansion of solid and establish their relation.
17. Describe how the cubical expansivity of a liquid can be determined by the use of balanced columns.
18. Distinguish between real and apparent expansion of liquid. Describe with mathematical detail, a method to determine real expansivity of a liquid.
19. Describe a method to determine the linear expansivity of a solid. Can the cubical expansivity be derived from this value?
20. Define linear and cubical expansivities of solids. Derive an expression for the variation in density of a solid when its temperature is raised from [latex]\theta_1^oC[/latex] to [latex]\theta_2^oC[/latex].
21. Define linear, superficial and cubical expansivities. Show that [latex]\beta 2\alpha[/latex] where [latex]\alpha[/latex] and [latex]\beta[/latex] are linear and superficial expansivities.
22. Why do substances expand on heating? Show that [latex]\alpha = \frac{\gamma}{3}[/latex], where [latex]\alpha[/latex] and [latex]\gamma[/latex] are the coefficients of linear and cubical expansions of a substance.
23. Obtain an expression for the change in density of a gas due to the thermal expansion.

NUMERICAL PROBLEMS

1. A glass flask of volume 400 cm³ is just filled with mercury at 0^oC. How much mercury overflows when the temperature of the system is raised to 80^oC? The coefficient of cubical expansivity of glass is 1.2 x 10^{-5 o}C^-1 and that of mercury is 1.8 x 10^{-5 o}C^-1. Ans: 2 x 10^-7 m³
2. A glass flask with volume 200 cm³ is filled to the brim with mercury at 20^oC. How much mercury overflows when the temperature of the system is raised to 100^oC? (Linear expansivity of glass = 0.4 x 10^-5 K^-1, cubical expansivity of mercury = 18 x 10^-5 K^-1). Ans: 2.688 cm³
3. A glass vessel of volume 50 cm³ is filled with mercury and is heated from 20^oC to 60^oC. What volume of mercury will overflow? Cubical expansivity of glass = 1.8 x 10^-6 K^-1 and cubical expansivity of mercury = 1.8 x 10^-4 K^-1. Ans: 0.3564 cm³
4. A glass flask of volume 500 cm³ is just filled with mercury at 0^oC. how much mercury overflows when the temperature of the system is raised to 80^oC? Ans: 0.24 cm³
5. A copper vessel with a volume of exactly 100 m³ at a temperature of 15^oC is filled with glycerine. If the temperature rises to 25^oC, how much glycerine will spill out? Ans: 0.48 m³
6. An iron rod of length 100 m at 10^oC is used to measure a distance of 2 km on a day when the temperature is 40^oC. Calculate the error in measuring the distance. [latex](\alpha[/latex] for iron = 12 x 10^{-6 o}C^-1). Ans: 72 cm
7. The marking on an aluminium ruler and a brass ruler are perfectly aligned at 0^oC. How far apart will the 20.0 cm marks be on the two rulers at 100^oC, if precise alignment of the left-hand ends of the rulers is maintained? Coefficient of linear expansion of aluminium and brass are 2.4 x 10^-5 K^-1 and 2.0 x 10^-5 K^-1 respectively. Ans: 0.008 cm
8. The length of an iron rod is measured by a brass scale. When both of them are at 10^oC, the measured length is 50 cm. What is the length of the rod of 40^oC when measured by the brass scale at 40^oC? [latex](\alpha[/latex] for brass = 24 x 10^{-6 o}C^-1,[latex]\alpha[/latex] for iron = 16 x 10^{-6 o}C^-1). Ans: 49.98 cm
9. A second pendulum made of brass keeps correct time at 10^oC. How many seconds it will lose or gain per day when the temperature of its surrounding rises to 35^oC? [latex](\alpha[/latex] for brass =[latex]2\times 10^{-5}[/latex]  ^oC^-1). (2074 ‘A’)Ans: 21.168 s lose per day
10. A brass pendulum clock keeps correct time at 15^oC. How many seconds per day it will lose or gain at 0^oC? [latex](\alpha [/latex] for brass = [latex]2\times 10^{-5}K^{-1})[/latex] Ans: 12.96 s gain
11. An iron pendulum clock keeps correct time at 20^oC. How many seconds will it gain or lose per day when temperature rises to 30^oC? (2069 ‘S’)Ans: 5.18 s per day
12. The pendulum of a clock is made of brass. If the clock keeps correct time at 15^oC, how many seconds per day will it lose at 20^oC? Ans: 4 s
13. A pendulum clock made of iron keeps correct time at 15^oC. How many seconds will it lose or gain per day when the temperature rises to 35^oC? Ans: 20.7 s
14. A clock which has a brass pendulum beats seconds correctly when the temperature of the room is 30^oC. How many seconds will it gain or lose per day when the temperature of the room falls to 10^oC? [latex](\alpha[/latex] for brass = 0.000018 ^oC^-1). Ans: 16.92 s gain
15. A steel wire 8m long and 4 mm in diameter is fixed to two rigid supports. Calculate the increase in tension when the temperature falls by 10^oC. (Young’s modulus of elasticity of steel = 2 x 10¹¹ N/m² and linear expansivity of steel = 1.2 x 10^-5 K^-1). Ans: 302.4 N
16. A copper wire of diameter 0.5 mm is stretched between two points at 25^oC. Calculate the increase in tension in the wire if the temperature falls to 0^oC. (Young’s modulus for copper = 1.2 x 10¹¹ Nm^-2), linear expansivity for copper = 18 x 10^-6 K^-1). Ans: 10.6 N
17. The density of silver at 0^oC is 10310 kgm^-3 and the coefficient of linear expansion is 0.000019/^oC. Calculate its density at 100^oC. Ans: 10251.57 kg/m³
18. Using the following data, determine the temperature at which wood will just sink in benzene. Density of benzene at 0^oC = 9.0 x 10² Kgm^-3, Density of wood at 0^oC = 8.8 x 10² Kgm^-3. (Cubical expansivity of benzene = 1.2 x 10^-3 K^-1, Cubical expansivity of wood = 1.5 x 10^-4 K^-1). Ans: 21.07^oC
19. A brass rod of length 0.40 m and steel rod of length 0.60 m, both are initially at 0^oC are heated to 75^oC. If the increase in length is the same for both the rods, calculate the linear expansivity of brass. The linear expansivity of steel is 12 x 10^{-6 o}C^-1. Ans: 18 x 10^{-6 o}C^-1