The temperature of n moles of an ideal gas is increased from T to 4 T through a process for which pressure P = a T − 1 , where a is a constant. The work done by the gas is

Step-by-step solution

According to ideal gas equation P V = n R T or V ⁡ = n R T ⁡ P ⁡ ∵ P ⁡ = a T ⁡ Given … i ∵ V ⁡ = n R ⁡ T ⁡ 2 a ⇒ dV = 2nRT a dT Work done by the gas, dW = PdV or W = ∫ T ⁡ 4 T ⁡ a T ⁡ 2 n R ⁡ T ⁡ a d T ⁡ … Using (i) and (ii) = 2 n ⁡ R ⁡ T ⁡ T ⁡ 4 T ⁡ = 6 n R T ⁡