Question

An ideal diatomic gas `(gamma=7/5)` undergoes a process in which its internal energy relates to the volume as `U=alphasqrtV`, where `alpha` is a constant.
(a) Find the work performed by the gas to increase its internal energy by 100J.
(b) Find the molar specific heat of the gas.

Answer 1

Correct Answer - A::B
`UpropsqrtV`
As `UpropT`
`:.` `TpropV^(1//2)`
or `TV^(-1//2)=` constant
or `pV^(1//2)=` constant
Comparing with `pV^x=` constant, we have
`x=1/2`
`:.` Molar specific heat
`C=(R)/(gamma-1)+(R)/(1-x)`
`=(R)/(7//5-1)+(R)/(1-1//2)`
`=5/2R+2R=(9R)/(2)`
`Q=nCDeltaT`
`DeltaU=nC_VDeltaT`
`:.` `W=Q-DeltaU=n(C-C_V)DeltaT`
`(W)/(DeltaU)=(C-C_V)/(C_V)`
`:.` W=((C-C_V)/(C_V))DeltaU`
`=((9//2-5//2)/(5//2))(100)=800J`