A gas undergoes a change according to the law P = P₀eᵃᵇ . The bulk modulus of the gas is

The correct option is aPV.

Step-by-step Explanation:

The pressure of the gas changes with volume according to the exponential relation:
$P=P_0{e}^{-aV}$
where $P$ is the pressure, $V$ is the volume, and $P_0$ and $a$ are constants.

The bulk modulus ($B$) of a gas is defined as:
$B=-V\frac{dP}{dV}$

First, we find the derivative of pressure with respect to volume, $\frac{dP}{dV}$:
$\frac{dP}{dV}=\frac{d}{dV}\left(P_0{e}^{-aV}\right)$
$\frac{dP}{dV}=P_0\cdot (-a)e^{-aV}$
$\frac{dP}{dV}=-a\left(P_0{e}^{-aV}\right)$
$\frac{dP}{dV}=-aP$

Next, we substitute this derivative back into the expression for the bulk modulus:
$B=-V(-aP)$
$B=aPV$

Thus, the bulk modulus of the gas is $aPV$.