Question

The densities of two substances are in the ratio $2:3$ and the specific heats are in the ratio $1:2$ respectively. The ratio of their heat capacities per unit volume is

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

Answer 1

The correct option is B $1:3$

Given: Ratio of densities of two substances = 2:3

Ratio of specific heat = 1:2

Solution: Thermal capacity of a substance is given by,

$=ms$

Ratio of the thermal capacities is given for the two substances is given by,

$=\frac{m_1{s}_1}{m_2{s}_2}=\frac{H_1}{H_2}$ (1)

Mass can be written as the product of volume and density.

So, equation (1) can be written as,

$=\frac{{\rho }_1{v}_1{s}_s}{{\rho }_2{v}_2{s}_2}$

where $\rho$ is the density and v is the volume.

Ratio for per unit volume we get,

$=\frac{{\rho }_1{s}_1}{{\rho }_2{s}_2}$

$=\frac{2}{3}\times \frac{1}{2}$

$=\frac{1}{3}$

Hence, the correct option is (B).