An ideal gas at pressure 2.5 × 105 Pa and temperature 300 K occupies 100 cc. It is adiabatically compressed to half its original volume. Calculate (a) the final pressure, (b) the final temperature and (c) the work done by the gas in the process. Take γ = 1.5.

Sol. P base 1 = 2.5 × 10^5 Pa, V base 1 = 100 cc, T base 1 = 300 k (a) P base 1V base 1^γ = P base 2V base 2^γ ⇒ 2.5 × 10^5 × V^1.5 = (V/2)^1.5 * P base 2 ⇒ P base 2 = 2^1.5 * 2.5 * 10^5 = 7.07 * 10^5 = 7.1 * 10^5 (b) T base 1V base 1^γ-1 = T base 2V base 2^ γ-1 ⇒ 300 * (100)^1.5 – 1 = T base 2 = (50)^1.5 - 1 ⇒ T base 2 = 3000/7.07 = 424.32 k = 424 k (c) Work done by the gas in the process W = mR/γ-1[T base 2 – T base 1] = P base 1V base 1/T(γ-1)[ T base 2 – T base 1] = 2.5 * 10^5 * 100 * 10^-6/300(1,5 - 1)[424 - 300] = 2.5 * 10/300 * 0.5 * 124 = 20.72 = 21 J