Question

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

Answer 1

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