Question

A and B are made up of an isotropic medium. Both A and B are of equal volume. Body B has a cavity as shown in figure b. Which of the following statements is true?
A. Expansion in volume of A > expansion in B
B. Expansion in volume of B > expansion in A
C. Expansion in A = expansion in B
D. None of these

Answer 1

Here both the bodies will subjected to the thermal expansion and we will compare the amount of the expansion in both the bodies A and B. Thermal expansion will take place in both the boxes and the expression for the thermal expansion of the isotropic body is given by $\Delta V = {V_\gamma }\Delta T$.

Complete answer:
So, in the expression for the thermal expansion of the isotropic body, the volumetric expansion will be dependent on the volume of the body and the change in the temperature. This shows that the expansion will be dependent on the volume of the body and will not be dependent on the shape and size of the body.

Here the change in the temperature is the same for both the boxes and it is also given in the question that both boys $A$ and $B$ have the same volume. So logically we see that there is no change in the volume of the two boxes and also there is no separate change in the temperature, they are subjected to the same change in the temperature.

So according to the expression of the thermal expansion of the isotropic body, the expansion in A is the same as that of the expansion in B.

So, the correct answer is “Option C”.

Note:
Here is a mention of the isotropic substance. As we know that the volumetric thermal expansion coefficient is the most basic thermal expansion coefficient. In general, the substances contract or expand when they are subjected to the temperature change and when this contraction or the expansion is occurring in all directions then the substance is called as isotropic.