Paragraph A thermally insulating cylinder has a thermally insulating and frictionless movable partition in the middle, as shown in the figure below. On each side of the partition, there is one mole of an ideal gas, with specific heat at constant volume, C_ V =2 R . Here, R is the gas constant. Initially, each side has a volume V₀ and temperature T₀ . The left side has an electric heater, which is turned on at very lo

Step-by-step solution

Writing C V in terms of degree of freedom of the gas f , we get, C V = f 2 R = 2 R ⇒ f = 4 , Therefore,​ adiabatic index of gas will be given by,​​​​​​ γ = 1 + 2 f = 1 + 2 4 = 3 2 The gas of the right portion has undergone through an adiabatic process so, T i V i γ - 1 = T f V f γ - 1 ⇒ T 0   V 0 3 2 - 1 = T R V 0 2 3 2 - 1 ⇒ T R = 2 T 0 ⇒ T R T 0 = 2 Work done by the gas 2 , = - ∆ U = - n C V T f - T i = - 1 2 R 2 T 0 - T 0 = - 2 2 - 2 R T 0 So work done by the gas