$5\mathrm{.}23$ The data listed below are claimed for power cycles operating between hot and cold reservoirs at $1000$ K and $400$ K $,$ respectively. For each case determine whether such a cycle is in keeping with the first and second laws of thermodynamics.

a$.Q_H=300kJ,W_{\text{c}\text{y}\text{c}\text{l}\text{e}}=160kJ,Q_C=140kJ.$

b$.Q_H=300kJ,W_{\text{c}\text{y}\text{c}\text{l}\text{e}}=180kJ,Q_C=120kJ.$

c$.Q_H=300kJ,W_{\text{c}\text{y}\text{c}\text{l}\text{e}}=170kJ,Q_C=140kJ.$

d$.Q_H=300kJ,W_{\text{c}\text{y}\text{c}\text{l}\text{e}}=200kJ,Q_C=100kJ$