A sample of gas at temperature T is adiabatically expanded to double its volume. The work done by the gas in the process is (given, = 3 2 ):

Step-by-step solution

For an adiabatic process, the relation between temperature and volume is TV^ - 1 = constant . T₁ V₁^ - 1 = T₂ V₂^ - 1 Substituting the given values, T₁ = T , V₁ = V , V₂ = 2V , and = 3 2 : T (V)^ 3 2 - 1 = T₂ (2V)^ 3 2 - 1 T V^ 1 2 = T₂ (2V)^ 1 2 T₂ = T 2 The work done by the gas in an adiabatic process for 1 mole is given by: W = R(T₁ - T₂) - 1 W = R (T - T 2 ) 3 2 - 1 W = RT (1 - 1 2 ) 1 2 W = 2RT (1 - 1 2 ) W = RT(2 - 2 ) Answer: W = RT[2 - 2 ]