A sample of gas `(gamma = 1.5)` is taken through an adiabatic process in which the volume is compressed from `1600 cm^(3) to 400 cm^(3)`. If the initial pressure is `150 kPa`, (a) what is the final pressure and (b) how much work is done by the gas in the process?

Explanation

(a) For the adiabatic process,
`p_1 V_1 = p_2 V_2gamma`.
Thus, p_2 = p_1(V_1 / V_2)gamma` = `(150 Kpa) (1600 cm ^(3) / 400 cm^(3))^(3/2) = 1200 kPa.`
(b) Work done by the gas in an adiabatic process is ` W =p_1 V_1 - p_2 V_2 / gamma-1`
= (150 kPa ) (1600 cm^(3) - (1200 kPa ) (400 cm^(3) / 1.5 - 1`
`= 240 J - 480 J / 0.5 = - 480 J`.