The work done by `1` mole of ideal gas during an adiabatic process is (are ) given by :

Options

A. `W=C_(v)(T_(f)-T_(i))`
B. `W=(P_(f)V_(f))/(gamma-1)[1+(P_(f))/(P_(i))]^(gamma-1)`
C. `W=(P_(f)V_(f))/(gamma-1)[1-((P_(i))/(P_(f)))^((gamma-1)/(gamma))]`
D. `W=(P_(f)V_(f)-P_(i)V_(i))/(gamma-1)`

Answer

A, C, D

Explanation

`W=(nR)/(gamma-1)xx[T_(f)-T_(i)]=G_(v)[T_(f)-T_(i)]`
`=(P_(f)V_(f)-P_(i)V_(i))/(gamma-1) ( :' PV=nRT)`
`=(P_(f)V_(f))/(gamma-1)[1-((P_(i)V_(i))/(P_(f)V_(f)))]`
`=(P_(f)V_(f))/(gamma-1)[1-(P_(i))/(P_(f))xx((P_(f))/(P_(i)))^(1/gamma)]( :' PV^(gamma)`=constant)
`=(P_(f)V_(f))/(gamma-1)[1-(P_(i)^(1-1/gamma))/(P_(f)^(1-1/gamma))] =(P_(f)V_(f))/(gamma-1)[1-((P_(i))/(P_(f)))^((gamma-1)/(gamma))]`