Question

Two bodies made of the same material have the same external dimensions and appearance, but one is solid and the other is hollow. When their temperature is increased, is the overall volume expansion the same or different? Why?

Short answer

The volume expansion is same for both the bodies.

Step-by-step solution

Expansion in volume due to thermal energy

The formula of volume expansion due to thermal energy is $\mathbf{\delta V}\mathbf{=}\mathbf{V}\mathbf{\times }\mathbf{\beta }\mathbf{\times }\mathbf{\delta T}$.

For the same coefficient of expansion $\mathbf{\left(}\mathbf{\beta }\mathbf{\right)}$and change in temperature $\mathbf{\left(}\mathbf{\delta T}\mathbf{\right)}$, the change in volume $\mathbf{\left(}\mathbf{\delta V}\mathbf{\right)}$will depend upon the volume $\left(V\right)$.

As both the bodies occupy the same volume, they will also expand in the same way. Hence, the overall volume expansion is same for both type of bodies.