Question

The ratio of the densities of the bodies is $3:4$ and ratio of specific heats is $4:3$. Find the ratio of their thermal capacities for unit volume?

• A. $1:1$
• B. $1:2$
• C. $3:1$
• D. $1:4$

Answer 1

The correct option is A $1:1$

Given that,
$\frac{{\rho }_1}{{\rho }_2}=\frac{3}{4}$

And ratio of specific heats is
$\frac{S_1}{S_2}=\frac{4}{3}$

Thermal capacity $=m\times S$

Thermal capacity per unit volume is defined as

$C=\rho \times S$

$\Rightarrow \frac{C_1}{C_2}=\frac{{\rho }_1{S}_1}{{\rho }_2{S}_2}$

$\therefore \frac{C_1}{C_2}=\frac{3}{4}\times \frac{4}{3}=\frac{1}{2}$

Ans : $\left(\text{A}\right)$