An ideal gas expands from an initial temperature `T_(1)` to a final temperature `T_(2)`. Prove that the work done by the gas is `C_(V) (T_(2) - T_(2))`.

Explanation

We have `Delta U = int_(T_(1))^(T_(2)) C_(v) dT - C_(v) (T_(2) - T_(1))`
Since the process is adiabatic, `dQ = 0`
`Delta Q = Delta U + Delta W`
`:. Delta W = - Delta U = - C_(v) (T_(2) - T_(1)) = C_(v) (T_(1) - T_(2))`