Molar heat capacity of an ideal gas in the process `PV^(x)` = constant , is given by : `C = (R)/(gamma-1) + (R)/(1-x)`. An ideal diatomic gas with `C_(V) = (5R)/(2)` occupies a volume `V_(1)` at a pressure `P_(1)`. The gas undergoes a process in which the pressure is proportional to the volume. At the end of the process the rms speed of the gas molecules has doubled from its initial value.
The molar heat capacity of the gas in the given process is :-

Options

A. `3R`
B. `3.5R`
C. `4R`
D. `2.5R`

Answer

A

Explanation

`P alpha V implies PV^(-1) = "constant" implies x = -1`
`implies C = C_(V) +(R)/(2) = (5R)/(2) + (R)/(2) = 3R`