Question

The densities of two substances are in the ratio 1 : 2 and their specific heat in the ratio 2 : 3. Compare their thermal capacities if their volumes are in the ratio 3 : 4.

Answer 1

Given, ratio of densities, $\frac{{\rho }_1}{{\rho }_2}=\frac{1}{2}$ ; ratio specific heat, $\frac{S_1}{S_2}=\frac{2}{3}$ and ratio of volumes, $\frac{V_1}{V_2}=\frac{3}{4}$

Thermal capacities are , $c_1=m_1{S}_1=\left({\rho }_1{V}_1\right)S_1$ and $c_2=m_2{S}_2=\left({\rho }_2{V}_2\right)S_2$

Thus, $\frac{c_1}{c_2}=\frac{{\rho }_1}{{\rho }_2}\times \frac{V_1}{V_2}\times \frac{S_1}{S_2}=\left(1/2\right)\left(3/4\right)\left(2/3\right)=1/4$