An ideal diatomic gas occupies a volume V1 at a pressure P1. The gas undergoes a process in which the pressure is proportional to the volume. At the end of process the rms speed of the gas molecules has doubled from its initial value then the heat supplied to the gas in the given process is :

Explanation

In this problem, the process involves the pressure of the gas being proportional to the volume, which suggests a linear relationship. The rms speed doubling implies that the temperature has increased by a factor of four (since rms speed is proportional to the square root of temperature). For an ideal diatomic gas, this means the internal energy changes significantly. The correct calculation of heat supplied considers the change in internal energy and the work done, leading to 9 P1V1. Options A, B, and D fail to correctly account for the relationships between the thermodynamic variables involved.