An ideal gas is taken through a cyclic process A B C A . The process A B is an isobaric expansion, B C is a linear process on the P-V indicator diagram, and C A is an isochoric process. The coordinates of the states are A (2 L , 400 kPa ) , B (5 L , 400 kPa ) , and C (2 L , P_C) . If the net work done by the gas in the cycle is -450 J , what is the value of the pressure P_C ?

Step-by-step solution

The net work done in the cyclic process is the sum of the work done in each individual process: W_ net = W_ AB + W_ BC + W_ CA 1) Process A B is an isobaric expansion at P = 400 kPa : W_ AB = P V = 400 10^3 Pa (5 - 2) 10⁻³ m ^3 = 1200 J 2) Process B C is a linear process from V = 5 L to V = 2 L : The work done is the area under the P-V graph (a trapezium): W_ BC = 1 2 (P_B + P_C) (V_C - V_B) W_ BC = 1 2 (400 + P_C) 10^3 (2 - 5) 10⁻³ = -1.5 (400 + P_C) J 3) Process C A is isochoric ( V = 0 ): W_ CA = 0 J Equating th