For adiabatic expansion, the pressure $\"\"$ and volume $\"\"$ are related by the equation $\"\"$ , where $\"\"$ is a constant.

At an instant, volume $\"\"$ and the pressure $\"\"$ .

Rate of change of pressure $\"\"$ .

Here the negative sign indicates that the pressure is decreasing.

Consider $\"\"$ .

Differentiate on each side with respect to $\"\"$ .

$\"\"$

Substitute $\"\"$ and $\"\"$ in the above equation.

$\"\"$

Therefore, the volume is increasing at a rate of $\"\"$ cm³/min.

The volume is increasing at a rate of $\"\"$ cm³/min.