Answer to Question #303834 in Mechanical Engineering for koki

Question

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

Answer 1

Solution;

Given;

$Q_1=100kJ,T_1=500K$

$Q_2=50kJ,T_2=400K$

$Q_3=-100kJ,T_3=300K$

For a reversible cycle;

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

Take $Q_4,T_4$ for the reverse process;

Hence;

$\frac{Q_1}{T_1}+\frac{Q_2}{T_2}+\frac{Q_3}{T_3}+\frac{Q_4}{T_4}=0$

$\frac{100}{500}+\frac{50}{400}+\frac{-100}{300}+\frac{Q_4}{T_4}=0$

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