Obtain an expression for the work done in a adiabatic process.

Explanation

In an adiabatic process, change in pressure, volume and temperature takes place under thermal isolation.
For an adiabatic process, PV.=K where `gamma=(C_(P))/(C_(V))` is known as the ratio of specific beats of a gas.
For a change of coordinates from `(P_(1)V_(1))" to "(P_(2)V_(2)),P_(1)V_(1)^(gamma)=P_(2)V_(2)^(gamma),P=(K)/(V^(gamma))`
Work done `=W=underset(V_(1))overset(V_(2))intPdV`
i.e., `W=Kunderset(V_(1))overset(V_(2))int(dV)/(V^(gamma))=(K)/(1-gamma)[(1)/(V_(2)^(gamma-1))-(1)/(V_(1)^(gamma-1))]`
`=(1)/(1-gamma)[(K)/(V_(2)^(gamma-1))-(K)/(V_(1)^(gamma-1))]=(1)/(1-gamma)[(P_(2)V_(2)^(gamma))/(V_(2)^(gamma-1))-(P_(1)V_(1)^(gamma))/(V_(1)^(gamma-1))]=(1)/(1-gamma)[P_(2)V_(2)-P_(1)V_(1)]`
`:.W=((1)/(1-gamma))muR(T_(2)-T_(1))=[(muR)/(gamma-1)][T_(1)-T_(2)]`