An ideal gas whose adiabatic exponent is γ is expanded according to the law p= αV where α is a constant. For this process the bulk modulus of the gas is

The correct option/answer is: p

To find the bulk modulus of the gas during this process, we start with the definition of the bulk modulus ($B$).
The bulk modulus is defined as:
$B=-V\frac{dp}{dV}$

The gas expands according to the given law:
$p=\alpha V$
where $\alpha$ is a constant.

To find $\frac{dp}{dV}$, we differentiate the equation $p=\alpha V$ with respect to volume $V$:
$\frac{dp}{dV}=\frac{d}{dV}\left(\alpha V\right)=\alpha$

Now, we substitute this derivative back into the definition of the bulk modulus:
$B=-V\left(\alpha \right)$
$B=-\alpha V$

Since $p=\alpha V$, we can replace $\alpha V$ with $p$:
$B=-p$

In physics, the magnitude of the bulk modulus represents the resistance of a substance to compression. The negative sign simply indicates that an increase in pressure causes a decrease in volume (and vice versa). Taking the magnitude of the bulk modulus for this process:
$\left|B\right|=p$

Thus, the bulk modulus of the gas for this process is $p$.