Thermal expansion of solids, liquids and gases — practice questions

Question 1 · difficulty L2 · understanding

A steel rod of length $$1 \mathrm{~m}$$ and cross sectional area $$10^{-4} \mathrm{~m}^{2}$$ is heated from $$0^{\circ} \mathrm{C}$$ to $$200^{\circ} \mathrm{C}$$ without being allowed to extend or bend. The compressive tension produced in the rod is ___________ $$\times 10^{4} \mathrm{~N}$$. (Given Young's modulus of steel $$=2 \times 10^{11} \mathrm{Nm}^{-2}$$, coefficient of linear expansion $$=10^{-5} \mathrm{~K}^{-1}$$ )

Question 2 · difficulty L2 · understanding

A faulty thermometer reads $5^{\circ} \mathrm{C}$ in melting ice and $95^{\circ} \mathrm{C}$ in stream. The correct temperature on absolute scale will be __________ $\mathrm{K}$ when the faulty thermometer reads $41^{\circ} \mathrm{C}$.

Question 3 · difficulty L2 · understanding

A hole is drilled in a metal sheet. At $$\mathrm{27^\circ C}$$, the diameter of hole is 5 cm. When the sheet is heated to $$\mathrm{177^\circ C}$$, the change in the diameter of hole is $$\mathrm{d\times10^{-3}}$$ cm. The value of d will be __________ if coefficient of linear expansion of the metal is $$1.6\times10^{-5}/^\circ$$C.

Question 4 · difficulty L2 · understanding

The resistances of the platinum wire of a platinum resistance thermometer at the ice point and steam point are $$8 \Omega$$ and $$10 \Omega$$ respectively. After inserting in a hot bath of temperature $$400^{\circ} \mathrm{C}$$, the resistance of platinum wire is :

• A. 10 $$\Omega$$
• B. 16 $$\Omega$$
• C. 8 $$\Omega$$
• D. 2 $$\Omega$$

Question 5 · difficulty L2 · understanding

On a temperature scale '$$\mathrm{X}$$', the boiling point of water is $$65^{\circ} \mathrm{X}$$ and the freezing point is $$-15^{\circ} \mathrm{X}$$. Assume that the $$\mathrm{X}$$ scale is linear. The equivalent temperature corresponding to $$-95^{\circ} \mathrm{X}$$ on the Farenheit scale would be:

• A. $$-148^{\circ} \mathrm{F}$$
• B. $$-48^{\circ} \mathrm{F}$$
• C. $$-63^{\circ} \mathrm{F}$$
• D. $$-112^{\circ} \mathrm{F}$$

Question 6 · difficulty L2 · understanding

The graph between two temperature scales P and Q is shown in the figure. Between upper fixed point and lower fixed point there are 150 equal divisions of scale P and 100 divisions on scale Q. The relationship for conversion between the two scales is given by :-

• A. $${{{t_P}} \over {100}} = {{{t_Q} - 180} \over {150}}$$
• B. $${{{t_P}} \over {180}} - {{{t_Q} - 40} \over {100}}$$
• C. $${{{t_Q}} \over {150}} = {{{t_P} - 180} \over {100}}$$
• D. $${{{t_Q}} \over {100}} = {{{t_P} - 30} \over {150}}$$

Question 7 · difficulty L2 · understanding

At what temperature a gold ring of diameter 6.230 cm be heated so that it can be fitted on a wooden bangle of diameter 6.241 cm ? Both the diameters have been measured at room temperature (27$$^\circ$$C). (Given : coefficient of linear thermal expansion of gold $$\alpha$$ L = 1.4 $$\times$$ 10 $$-$$5 K $$-$$1 )

• A. 125.7$$^\circ$$C
• B. 91.7$$^\circ$$C
• C. 425.7$$^\circ$$C
• D. 152.7$$^\circ$$C

Question 8 · difficulty L2 · understanding

A solid metallic cube having total surface area 24 m 2 is uniformly heated. If its temperature is increased by 10$$^\circ$$C, calculate the increase in volume of the cube. (Given $$\alpha$$ = 5.0 $$\times$$ 10 $$-$$4 $$^\circ$$C $$-$$1 ).

• A. 2.4 $$\times$$ 10 6 cm 3
• B. 1.2 $$\times$$ 10 5 cm 3
• C. 6.0 $$\times$$ 10 4 cm 3
• D. 4.8 $$\times$$ 10 5 cm 3

Question 9 · difficulty L2 · understanding

A bimetallic strip consists of metals A and B. It is mounted rigidly as shown. The metal A has higher coefficient of expansion compared to that of metal B. When the bimetallic strip is placed in a cold bath, it will :

• A. Neither bend nor shrink
• B. Bend towards the left
• C. Not bend but shrink
• D. Bend towards the right

Question 10 · difficulty L2 · understanding

Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R. Assertion A : When a rod lying freely is heated, no thermal stress is developed in it. Reason R : On heating, the length of the rod increases. In the light of the above statements, choose the correct answer from the options given below :

• A. A is true but R is false
• B. A is false but R is true
• C. Both A and B are true but R is NOT the correct explanation of A
• D. Both A and R are true and R is the correct explanation of A