Problem 10.94 Challenge

จาก \(W_{eng}= -W\)

\(W_{eng} =\) พื้นที่วงปิดแผนภาพ PV

\(W_{eng}= (2P)(V)\)

\(W_{eng}= 2PV\)

จาก \(\Delta U_{AB}= Q_{1} + W_{AB}\)

\(nc_{V}\Delta T = Q_{1} + 0; \Delta U = nc_{V}\Delta T and W = 0\)

\(Q_{1}=n(\frac{d}{2}R)(T_{B}- T_{A}); c_{V}=\frac{d}{2}R\)

\(Q_{1}=\frac{3}{2}(nRT_{B}- nRT_{A}); d = 3\)

\(Q_{1}=\frac{3}{2}(3PV-PV); PV = nRT\)

\(Q_{1} = 3PV\)

จาก \(\Delta U_{BC}= Q_{2} + W_{BC}\)

\(nc_{V}\Delta T = Q_{2} + W_{BC}; \Delta U = nc_{V}\Delta T\)

\(nc_{V}\Delta T = Q_{2} - 3P(2V - V); W = -P\Delta V\)

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

\(Q_{2}=\frac{3}{2}(nRT_{C}- nRT_{B}) + 3PV; d = 3\)

\(Q_{2}=\frac{3}{2}(6PV-3PV)+3PV; PV = nRT\)

\(Q_{2}=\frac{9}{2}PV+3PV\)

\(Q_{2} =\frac{15}{2}PV\)

จาก \(Q_{h}= Q_{1} + Q_{2} = 3PV +\frac{15}{2}PV =\frac{21}{2}PV\)

จาก \(e = \frac{W_{eng}}{|Q_{h}|}\)

\(e =\frac{2PV}{\frac{21}{2}PV}=\frac{4}{21}\) หรือ \(19.0% \;\blacksquare\)