Problem 10.95 Challenge

พิจารณาช่วง A → B

\(Q_{AB}= nRT_{A}\ln (\frac{5V}{V}); Isothermal Process\)

\(Q_{AB}= 5PVln(5); PV = nRT\)

พิจารณาช่วง B → C

\(Q_{BC}= nc_{P}\Delta T; Isobaric Process\)

\(Q_{BC}= n((\frac{d + 2}{2})R)\Delta T; c_{P}= (\frac{d + 2}{2})R\)

\(Q_{BC}= n((\frac{3 + 2}{2})R)(T_{C}- T_{B}); d = 3\)

\(Q_{BC}=\frac{5}{2}(nRT_{C}- nRT_{B})\)

\(Q_{BC}=\frac{5}{2}(PV-5PV); PV = nRT\)

\(Q_{BC}= -10PV\)

พิจารณาช่วง C → A

\(Q_{CA}= nc_{V}\Delta T; Isovolumetric Process\)

\(Q_{CA}=n((\frac{d}{2})R)\Delta T; c_{V}=(\frac{d}{2})R\)

\(Q_{CA}=n((\frac{3}{2})R)(T_{A}- T_{C}); d = 3\)

\(Q_{CA}=\frac{3}{2}(nRT_{A}- nRT_{C})\)

\(Q_{CA}=\frac{3}{2}(5PV-PV); PV = nRT\)

\(Q_{CA}= 6PV\)

จาก \(Q_{h}= Q_{CA}+ Q_{AB}= 6PV + 5PVln(5) = PV(6 + 5\ln (5))\)

จาก \(Q_{c}= Q_{BC}= -10PV\)

จาก \(e = 1 - \frac{|Q_{c}|}{|Q_{h}|}\)

\(e = 1 -\frac{10PV}{PV(6 + 5\ln (5))}\)

\(e = 1 -\frac{10}{6 + 5\ln (5)} = 0.289\) หรือ \(28.9% \;\blacksquare\)