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, (given γ = 3 2 ) :

Step-by-step solution

Work done by gas in adiabatic process is: W = - P 2 V 2 - P 1 V 1 γ - 1 = - n R T 2 - T 1 γ - 1 For an adiabatic process, T 1 V 1 γ - 1 = T 2 V 2 γ - 1 ⇒ T V 3 2 - 1 = T 2 2 V 3 2 - 1 ⇒ T V 1 2 = T 2 2 V 1 2 ⇒ T 2 = T 2 Now, work done is W = R T 1 - T 2 γ - 1 = R T - T 2 1 2 = R T 2 - 2