For an isothermal irreversible expansion of 1mole of a perfect gas, identicy the correct relation, where symbols have their usual meaning

Options

A. `/_\U=0`
B. `/_\H=0`
C. `q=RT(1-(P_(2))/(P_(1)))`
D. `w=RTln ((P_(2))/(P_(1)))`

Answer

A, B, C

Explanation

`/_\U=nC_(v)/_\T( :'T=0, /_\U=0)`
`/_\H=nC_(P) /_\T ( :'T=0,/_\H=0)`
`1^(st)` law `/_\U=q+w=0`
`:.q=-w`
`w=-int_(v_(1))^(v_(2)) P_("ext")dv`
`P_("ext")=P_(2)'w=-P_(2)(V_(2)-V_(1))`
`w=-P_(2)[(RT)/(P_(2))-(RT)/(P_(1))]`
`=-RT[1/(P_(2))/(P_(1))]`
`:.q=RT[1-(P_(2))/(P_(1))]`