A gaseous mixture consists of 1 mole of helium (monatomic) and 1 mole of oxygen (rigid diatomic) at an initial temperature T₀ and pressure P₀ . The mixture is adiabatically expanded until its pressure drops to P₀ 8 . The work done by the gas mixture during this expansion is:

Step-by-step solution

First, we find the effective properties of the gas mixture. The total number of moles is n = 1 + 1 = 2 . The molar heat capacity at constant volume for the mixture is: C_ v, mix = n₁ C_ v1 + n₂ C_ v2 n₁ + n₂ = 1 ( 3 2 R ) + 1 ( 5 2 R ) 2 = 2R The molar heat capacity at constant pressure is C_ p, mix = C_ v, mix + R = 3R . Thus, the effective adiabatic exponent is = C_ p, mix C_ v, mix = 3R 2R = 3 2 . For an adiabatic process, the temperature and pressure are related by T P^ 1- = constant . Here, 1- = 1 - 1.5 1.5 =