Two moles of a monatomic ideal gas are taken through a cyclic process shown on the P - T diagram. The process CA is represented as P T = constant. If the efficiency of the given cyclic process is 1 - x 1 2 ln 2 + 1 5 , then what is the value of x ?

Step-by-step solution

For process AB , T A = 300 K , T B = 600 K W = nR Δ T = nR T B - T A = 3 0 0 nR = 6 0 0 R Q = nC p Δ T = 2 × 5 2 R 3 0 0 = 1 5 0 0 R For process BC , W = nRT ln V f V i = nRT ln p i p f = nRT ln 2 = 1 2 0 0 R ln 2 For process CA , W = ∫ P d V = ∫ 6 0 0 3 0 0 K T 2 nRT K d T = - 2 nR 3 0 0 = - 1 2 0 0 R Q = nC v Δ T + W = 2 × 3 2 R - 3 0 0 - 1 2 0 0 R = - 9 0 0 R - 1 2 0 0 R = - 2 1 0 0 R η = 6 0 0 R + 1 2 0 0 R ln 2 - 1 2 0 0 R 1 5 0 0 R + 1 2 0 0 R ln 2 η = 1 - 2 1 1 2 ln 2 + 1 5 Comparing with given equation, x =