"A diesel engine has a compression ratio of 22:1. The conditions in the cylinder at the start of compression are p = 101.2 kPa and T = 325 K. Calculate the pressure and temperature at the end of compression, assuming that the process is isentropic." r_c = 22 "Composition" y_O2 = 0.2095 y_N2 = 0.7905 "Starting Point - 1" P_1 = 101.3 "[kPa]" T_1 = 325 "[kPa]" v_1 = y_O2 * VOLUME(O2,T=T_1,P=P_1)+y_N2 * VOLUME(N2,T=T_1,P=P_1) cp_1 = y_O2 * CP(O2,T=T_1)+y_N2 * CP(N2,T=T_1) cp_1 - cv_1 = R# gamma_1 = cp_1/cv_1 u_1 = y_O2 * INTENERGY(O2,T=T_1)+y_N2 * INTENERGY(N2,T=T_1) s_1 = y_O2 * ENTROPY(O2,T=T_1,P=y_O2*P_1)+y_N2 * ENTROPY(N2,T=T_1,P=y_N2*P_1) "End Point - 2" v_2 = y_O2 * VOLUME(O2,T=T_2,P=P_2)+y_N2 * VOLUME(N2,T=T_2,P=P_2) v_2 = v_1 / r_c cp_2 = y_O2 * CP(O2,T=T_2)+y_N2 * CP(N2,T=T_2) cp_2 - cv_2 = R# gamma_2 = cp_2/cv_2 u_2 = y_O2 * INTENERGY(O2,T=T_2)+y_N2 * INTENERGY(N2,T=T_2) s_2 = y_O2 * ENTROPY(O2,T=T_2,P=y_O2*P_2)+y_N2 * ENTROPY(N2,T=T_2,P=y_N2*P_2) s_2=s_1 "Work done per kg" w_12 = (u_2 - u_1)/molarmass(air) "Compare with polytropic process" {gamma=(gamma_1+gamma_2)/2} "Exercise value" gamma=1.4 "Check against text" (T_2a/T_1)=(P_2a/P_1)^((gamma-1)/gamma) (T_1*P_2a)/(T_2a*P_1)=r_c