The ratio of P to V at any instant is constant and is equal to 1. for a monoatomic ideal gas undergoing a process. What is the molar heat capacity of the gas?

Options

A. `(3R)/2`
B. `(4R)/2`
C. `(5R)/2`
D. `0`

Answer

B

Explanation

From first law of Thermodynamics , `DeltaE=q+w implies nC_vdT=nCdT-PdV` .. (1)
Now according to process , P=V and according to ideal gas equation , PV=nRT
We have , `V^2=nRT`
On differentiating , 2VdV=nRdT and PdV=VdV=`(nRdT)/2`
So from first equation we have, `nC_vdT=nCdT-(nRdT)/2`
So, `C_v=C-R/2` Hence C`=(4R)/2`