When an ideal diatomic gas is heated at constant pressure, the fraction of heat energy supplied which is used in doing work to maintain pressure constant is

Options

A. `3/5`
B. `2/5`
C. `2/7`
D. `4/7`

Answer

C

Explanation

Heat supplied `DeltaQ=dU+dW`
As `PV=RT implies PdV=RdT`
`implies dT=(PdV)/(R)`
Since, `DeltaQ = C_V (PdV)/(R)+PdV`
Work done at constant pressure, C
`DeltaW=PdV`
`implies (DeltaQ)/(DeltaW)=(C_V(PdV)/(R)+PdV)/(PdV)`
`implies (DeltaQ)/(DeltaW)=(C_V)/(R)+1`
For diatomic `C_V=(5R)/(2)`
`(DeltaQ)/(DeltaW)=5/2+1 implies (DeltaW)/(DeltaQ)=2/7`