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.

TInitial  = t K

Work, W = 9R

Ratio of specific heats, γ = C/ Cv = 4/3

In an adiabatic process, we have

W = R(TFinal – Tinitial) / (1-γ)

9R = R (TFinal – t) / (1 – 4/3)

TFinal – t = 9 (-1/3) = -3

TFinal  = (t-3) K

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