Consider a rectangular sheet of solid material of length $l=9 \mathrm{~cm}$ and width $d=4 \mathrm{~

Question

Consider a rectangular sheet of solid material of length $l=9 \mathrm{~cm}$ and width $d=4 \mathrm{~cm}$. The coefficient of linear expansion is $\alpha=3.1 	imes 10^{-5} \mathrm{~K}^{-1}$ at room temperature and one atmospheric pressure. The mass of sheet $m=0.1 \mathrm{~kg}$ and the specific heat capacity $C_{V}=900 \mathrm{~J} \mathrm{~kg}^{-1} \mathrm{~K}^{-1}$. If the amount of heat supplied to the material is $8.1 	imes 10^{2} \mathrm{~J}$ then change in area of the rectangular sheet is\

Professor PC Thomas Classes · Answer

(a) : $l=9 \mathrm{~cm}$, width, $d=4 \mathrm{~cm}, \alpha=3.1 	imes 10^{-5} \mathrm{~K}^{-1}$\ $ \begin{aligned} & m=0.1 \mathrm{~kg}, C=900 \mathrm{~J} / \mathrm{kg} \mathrm{~K} \ & H=8.1 	imes 10^{2} \mathrm{~J} \ & H=m C \Delta T \end{aligned} $ $$ \begin{array}{ll} 	herefore & 8.1 	imes 10^{2}=0.1 	imes 900 	imes \Delta T \Rightarrow \Delta T=9 \mathrm{~K} \ & \Delta A=2 A_{0} \alpha \Delta T \ & =9 	imes 4 	imes 10^{-4} 	imes 2 	imes 3.1 	imes 10^{-5} 	imes 9 \ & =2 	imes 10^{-6} \mathrm{~m}^{2} \end{array} $$