Question

3.A cylinder contains 0.085 m3 of gas at 1.032 bar and 38°C. The gas is compressed according to the law PVi3 - constant until the pressure is 5.5 bar. Determine the heat energy supplied or rejected during the process. For the gas take cv 0.715 kJ/kgK and R 0.287 kJ/kgK.

Answer 1

volume V_1 = 0.085 m^3 pressure P_1 = 1.032 bar Temperature T_1 = 38 degree C Gas is compressed according to PV^1.3 = k therefore k = constant the process PV^T = constant shows adiabatic process. In adiabatic process. Process does not involve transfer of heat so Q = 0, c_v = 0.715 KJ/Kg K R = 0.287 KJ/Kg k R = 0.287 KJ/Kg K therefore P_1 V^1.3_1 = P_2 V^1.3_2 V^1.3_2 = P_1/P_2 (V_1)^1.3 = 0.1876 times 0.041 = 0.0076 V_2 = 0.0234 m^3 work done = (PV^Y) (V^1 - Y - V^1 - Y_i)/1 - Y \r\n w = {(1.032) (0.085)^1.3} {(0.0234)^1 - 1.3 - (0.035)^1 - 1.3}/-(0.3) w = -{(103200) (0.085)^1.3} {3.086 - 2.096}/(30) w = -340409.997 times (0.085)^1.3 w = -13811.69 Joules therefore Heat supplied or rejected during adiabatic process is 0.