Please answer question according to the attached image. For the ideal gas which
ID: 1850826 • Letter: P
Question
Please answer question according to the attached image.
For the ideal gas which has gone through an isentropic process 1-right arrow 2, please prove the following relationship: 0.1 kg of air as an ideal gas with k=1.4 executes a Carnot refrigeration cycle. The isothermal expansion occurs at 250K with a heat transfer to the air of 3.5 KJ. The isothermal compression occurs at 300K to a final volume of 0.01m3 Draw a p-v and T-S diagram of the cycle. Find out the pressures at each of four principle states. Find out COP of the system.Explanation / Answer
the entropy change is S2-S1 = Cvln(T2/T1) + Rln(V2/V1) and S2-S1 = Cpln(T2/T1) - Rln(P2/P1) and R/Cv = K-1 and R/Cp = (K-1)/K for isentropic processes we have (T2/T1) = (V1/V2)^(K-1) and (T2/T1) = (P2/P1)^(K-1)/K equating both T2/T1 we get the given relation Pressure at final state is 0.1*0.287*300/0.01 = 861kPa = P4 P1 = 454.85 kPa 0.1*0.287*250ln(P2/P1) =3.5 => P2 = 740.83 kPa P3 = 1402.34 kPa COP of system is 1/(300/250-1) = 5