Question

In a carnot cycle operating between 307 and 17 degree Celsius the maximum and minimum pressures are 60 2.4 and 1.04 bar.clclculate the cycle efficiency and the work ratio.assume air yo be working fluid.

Answer 1

The cycle efficiency:

$$\eta=1-\frac{T_2}{T_1}=1-\frac{290}{580}=0.5$$

$$WR=\frac{W_{net}}{W_{gross}}$$

$$W_{net}=(T_1-T_2)(S_1-S_2)$$

4-a is isothermal, so

$$S_A-S_4=R\ln{\frac{P_4}{P_2}}=0.287\ln{\frac{62.4}{1.04}}=1.175\frac{kJ}{kg}$$

a-2 is isobaric, so

$$S_2-S_a=c_p\ln{\frac{T_1}{T_2}}=1.005\ln{\frac{580}{290}}=0.6966\frac{kJ}{kg}$$

$$W_{net}=(580-290)(1.175-0.696)=139.2\frac{kJ}{kg}$$

$$W_{gross}=T_1(S_1-S_4)+c_v(T_1-T_2)$$

$$W_{gross}=580(0.48)+0.718(580-290)=486.62\frac{kJ}{kg}$$

$$WR=\frac{139.2}{486.62}=0.286$$