PROBLEM $4$

A power cycle operating between two reservoirs receives energy $Q_H$ by heat transfer from hot

reservoir at $T_H=2000K$ and rejects heat energy $Q_C$ by heat transfer to a cold reservoir at $T_C=400K.$ For

each of the following case, determine whether the cycle operates reversibly, irreversibly, or

impossible

a$)Q_H=1000kJ,$ Wcycle $=850kJ$

b$)Q_H=2000kJ,Q_C=400kJ$

c$)W_{\text{c}\text{y}\text{c}\text{l}\text{e}}=1600kJ,Q_c=500kJ$

d$)Q_H=1000kJ,{}_{\text{c}\text{y}\text{c}\text{l}\text{e}}=30\%$

Note: for a power cycle $Q_H-Q_C=W_{cycl}$

Carnot efficincy for a power cycle ${}_{\text{c}\text{y}\text{c}\text{l}\text{e}\text{c}\text{a}\text{r}\text{n}\text{o}\text{t}}=1-\frac{T_c}{T_H}$

Cycle efficiency ${}_{\text{c}\text{y}\text{c}\text{l}\text{e}}=\frac{\text{W}\text{c}\text{y}\text{c}\text{l}\text{e}}{Q_H}=\frac{Q_H-Q_c}{Q_H}$