Question

In a process, the molar heat capacity of a diatomic gas is `(10)/(3) R`. When heat Q is supplied to the gas, find the work done by the gas
A. `(3Q)/(4)`
B. `(Q)/(4)`
C. `(Q)/(3)`
D. `(2Q)/(3)`

Answer 1

Correct Answer - B
We define molar heat capacity `C = Q=(DeltaT)`
But `DeltaU = (5/2 R) DeltaT`
`Delta T = (2DeltaU)/(5R)`
`C = (Q)/(DeltaT) = (5(Q)R)/(2DeltaU) = 10/3 R` (given)
`Q/(Delta U) = 4/3` ..(i)
From first law of thermodynamics
`DeltaU = Q-W` ..(ii)
From (i) and (ii) `Q/(Q-W) = 4/3`
We get `W = Q/4` .