Question #303834

in a reversible cycle 100 KJ of heat is recieved at 500K then a adiabatic expansion occurs to 400K at which temperature of 50 KJ of heat is recieved , then a further adibatic expansion at 300 K at which temperature of 100 KJ is rejected : (1)find the change in entropy which occurs as the system is restored to its initial state in the remainder of the cycle


1
Expert's answer
2022-02-28T11:10:09-0500

Solution;

Given;

Q1=100kJ,T1=500KQ_1=100kJ,T_1=500K

Q2=50kJ,T2=400KQ_2=50kJ,T_2=400K

Q3=100kJ,T3=300KQ_3=-100kJ,T_3=300K

For a reversible cycle;

dQT=0\oint\frac{dQ}{T}=0

Take Q4,T4Q_4,T_4 for the reverse process;

Hence;

Q1T1+Q2T2+Q3T3+Q4T4=0\frac{Q_1}{T_1}+\frac{Q_2}{T_2}+\frac{Q_3}{T_3}+\frac{Q_4}{T_4}=0

100500+50400+100300+Q4T4=0\frac{100}{500}+\frac{50}{400}+\frac{-100}{300}+\frac{Q_4}{T_4}=0

Q4T4=Δs4=8.33×103kJ/K\frac{Q_4}{T_4}=\Delta s_4=8.33×10^{-3}kJ/K



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