Question

The adiabatic bulk modulus of a diatomic gas at atmospheric pressure is

• A. $2.8\times {10}^5{\text{Nm}}^{-2}$
• B. $1{\text{Nm}}^{-2}$
• C. $1.4\times {10}^4{\text{Nm}}^{-2}$
• D. $1.4\times {10}^5{\text{Nm}}^{-2}$

Answer 1

The correct option is D $1.4\times {10}^5{\text{Nm}}^{-2}$

$\text{Bulk modulus}=\frac{\text{Stress}}{\text{Volumetric strain}}$

$K=\frac{-\Delta P}{\frac{\Delta V}{V}}=-V\frac{dP}{dV}$

For adiabatic process,


$\Rightarrow \frac{dP}{dV}=-\frac{\gamma P}{V}$

Now bulk modulus,

$K=-V(-\frac{\gamma P}{V})=\gamma P$

For diatomic gas, $\gamma =\frac{7}{5}$

Atmospheric pressure, $P=1.013\times {10}^5\text{Pa}$

$\Rightarrow K=\frac{7}{5}\times 1.013\times {10}^5\approx 1.4\times {10}^5{\text{Nm}}^{-2}$

Hence, $\left(D\right)$ is the correct answer.