Find the final temperature of one mole of an ideal gas which has an initial temperature t K. The gas does 9 R joules of work adiabatically. The ratio of specific heats of this gas at constant pressure and at constant volume is 4/3.

T_Initial  = t K

Work, W = 9R

Ratio of specific heats, γ = C_p / C_v = 4/3

In an adiabatic process, we have

W = R(T_Final – T_initial) / (1-γ)

9R = R (T_Final – t) / (1 – 4/3)

T_Final – t = 9 (-1/3) = -3

T_Final  = (t-3) K