Question

$C_p$ and $C_v$ are specific heats at constant pressure and constant volume respectively. It is observed that

$C_p-C_v=a$ for hydrogen gas

$C_p-C_v=b$ for nitrogen gas

The correct relation between $a$ and $b$ is

• A. $a=\frac{1}{14b}$
• B. $a=b$
• C. $a=14b$
• D. $a=28b$

Answer 1

The correct option is C

$a=14b$

Step 1. Given data

$C_p-C_v=a$ ……… $eq\left(1\right)$ [$C_p$ is the specific heat at constant pressure.]

$C_p-C_V=b$ ………$eq\left(2\right)$ [$C_v$ is the specific heat at constant volume']

Step 2. The formula of the specific heat.

Specific heat per unit mass, $\left(M_g\right)$

$C_p-C_v=\frac{R}{M_g}$ , [Where, $R$ is the Universal gas constant.]

By comparing this equation to the above equation, we get

For Hydrogen gas, $a=\frac{R}{2}$ …….$eq\left(3\right)$ [Molar mass of the hydrogen is $2gmmol{e}^{-1}$]

For Nitrogen gas, $b=\frac{R}{28}$ …….$eq\left(4\right)$ [Molar mass of the nitrogen is $28gmmol{e}^{-1}$]

Dividing the $eq\left(3\right)$, and $eq\left(4\right)$, we get

$\frac{a}{b}=14$

$a=14b$

Hence, the correct option is $\left(C\right)$.