Question

An insulated vessel contains four moles of an ideal, monatomic gas at absolute temperature To. The gas is placed in thermal contact with a heat reservoir at temperature T./3. Heat is exchanged between the reservoir and the gas until thermal equilibrium is established. (a) What is the equilibrium temperature of the gas? (b) is the process of heat exchange reversible or irreversible? Explain. (c) How does the pressure of the gas change during the process of heat exchange? Does the volume of the gas change? Explain. (d) Calculate the change in the entropy of the gas during the process of heat exchange. (You may leave the ideal gas constant R in the answer.) What is the physical significance of the sign of the result? (e) Show that the answer to part (d) is consistent with the second law of thermodynamics. You may find useful the inequality < > In 2+1, which holds for all 3 > 0 except =1.

Answer 1

To Equilibrium temperature of gas To 3 a 6 The procen of heat exchange is irreversible process. This is because heat transfer is not a property. Heat transfer is a path function. At constant volume: - Pp To =Pq Tz Pa Xo = To y la YIP + = 32 P₂ = 75 P → The pressure of the gas becomes one-third times that af initial pressure. No the volume of the gas does not change since the centainer in rigid (isochonic process). change in gas = Tz +R ln V2 Vi Ti JI ) + Ran oo entropy of the Cu lu 2 / R xdn (11) kun = 2 Rada (73) J I Knol. = -10647918 R - -10647918 x 8.314 TIK AS = -13.7008 Jl Knhol AS =413.7008 x 4 ) J lk E-54.8032 JIK - CSScanned with CamSchanner

Hegative sign indicates that the entropy of the gas decreases during the process. e Second law of thermodynamics states that net entropy of an inolated system neuer decreases. Now, considering the vessel and link (heat sources as inolated an system, Haak Albanet Q medT = T T (AS) heat reservoin = 4X10SRX 2/2 To ☆ To Jlkan 12R 12*8.314 JIK, = 99.768 ТІК (AS) Net (9 99.768 + (-54.8032) JIK = 44.9648 TIK . (AS) met > o Hence, proved. CSScanned with CamScanner