One mole of an ideal monatomic gas undergoes the process `p=alphaT^(1//2)`, where `alpha` is a constant.
(a) Find the work done by the gas if its temperature increases by 50K.
(b) Also, find the molar specific heat of the gas.

Answer

A, B

Explanation

(a) `p=alphaT^(1//2)`
or `pT^(-1//2)=cont ant`
`p^(1//2)V^(-1//2)=const ant`
`pV^-1=const ant`
`:.` `x=-1`
`DeltaW=((R)/(1-x))(DeltaT)`
`(8.31/2)(50)`
`=207.75J`
(b) `C=C_V+(R)/(1-x)=3/2R+R/2=2R`