P-V diagram of a diatomic gas is a straight line passing through origin. The molar heat capacity of the gas in the process will be

Options

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

Answer

B

Explanation

`PpropV`
`P=kV`,`K,` constant
`(nRT)/(V)=kV`
`nRT=kV^2`
`nRdT=k.2VdV`
`(dV)/(dT)=(nR)/(2kV)=(nR)/(2P)`
`dQ=dU+dW`
`nCdT=nC_VdT+PdV`
`C=C_V+(P)/(n)(dV)/(dT)=(3R)/(2)+(P)/(n).(nR)/(2P)`
`=(3R)/(2)+(R)/(2)=2R`