Consider a rectangular sheet of solid material of length $l = 9\ \text{cm}$ and width $d = 4\ \text{cm}$. The coefficient of linear expansion is $\alpha = 3.1\times10^{-5}\ \text{K}^{-1}$ at room temperature and one atmospheric pressure. The mass of the sheet is $m = 0.1\ \text{kg}$ and the specific heat capacity $C_v = 900\ \text{J kg}^{-1}\text{K}^{-1}$. If the amount of heat supplied to the material is $8.1\times10^2\ \text{J}$, then the change in area of the rectangular sheet is:
Answer: (A) $2.0\times10^{-6}\ \text{m}^2$
Temperature rise: $\Delta T = \dfrac{Q}{mc} = \dfrac{810}{0.1\times900} = 9\ \text{K}$.
Area expansion uses $\beta = 2\alpha$, with $A_0 = 9\times4 = 36\ \text{cm}^2 = 3.6\times10^{-3}\ \text{m}^2$:
$$\Delta A = 2\alpha A_0\Delta T = 2\times3.1\times10^{-5}\times3.6\times10^{-3}\times9 \approx 2.0\times10^{-6}\ \text{m}^2$$
Solution by Sreeraj P, M.Sc Physics