The molar heat capacity in a process of a diatomic gas if it does a work of `Q/4` when a heat of `Q` is supplied to it is

Options

A. `(2)/(5)R`
B. `(5)/(2)R`
C. `(10)/(3)R`
D. `(6)/(7)R`

Answer

c

Explanation

`dU=C_(v)dT=((5)/(2)R)dT`
`rArr dT=(2(dU))/(5R)`
From first law of thermodynamics, `dU=dQ=dW`
or `dU=Q-(Q)/(4)=(3Q)/(4)`
Now, molar heat capacity.
`C=(dQ)/(dT)=(Q)/(2((dU)/(5R)))=(5QR)/(2((3Q)/(4)))=(10)/(3)R`