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Question

Physics Question on Thermal Expansion

Each side of a box made of metal sheet in cubic shape is 'a' at room temperature 'T', the coefficient of linear expansion of the metal sheet is ' α\alpha^{\prime}. The metal sheet is heated uniformly, by a small temperature ΔT,\Delta T , so that its new temperature is T+ΔTT +\Delta T. Calculate the increase in the volume of the metal box.

A

3a3αΔT3 a ^{3} \alpha \Delta T

B

4a3αΔT4 a ^{3} \alpha \Delta T

C

4πa3αΔT4 \pi a ^{3} \alpha \Delta T

D

43πa3αΔT\frac{4}{3} \pi a ^{3} \alpha \Delta T

Answer

3a3αΔT3 a ^{3} \alpha \Delta T

Explanation

Solution

The correct option is(A): 3a3αΔT3 a ^{3} \alpha \Delta T.

ΔV=VγΔT\Delta V = V \gamma \Delta T
ΔV=3a3αΔT\Delta V =3 a ^{3} \alpha \Delta T