Question

A given quantity of an ideal gas is at pressure $P$ and absolute temperature $T$. The isothermal bulk modulus of the gas is

• A. $\frac{2P}{3}$
• B. $P$
• C. $\frac{3P}{3}$
• D. $2P$

Answer 1

The correct option is B $P$

Bulk modulus is given by
$K=\frac{\text{Stress}}{\text{Volumetric strain}}$

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

For isothermal process, $\text{PV = Constant}$.

Differentiating both sides,

$\Rightarrow PdV+VdP=0$

$\Rightarrow PdV=-VdP$

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

Now,
$K=-V\times \frac{dP}{dV}=-V(-\frac{P}{V})$

$\Rightarrow K=P$

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