a$)$ Evaluate the integral for the cycle shown below. Note the direction of heat flow indicated by the

arrows.

$o{\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}(\frac{Q}{T}{)}_{\text{r}\text{e}\text{v}}=$

Low remperature keservoir

$T_L=20C$

b$)$ Does the value you calculated makes sense given what you know about the Clausius inequality?

Explain why or why not.

c$)$ Using the Clausius inequality, calculate the minimum allowable value of $Q_H$ given the

temperature of the two reservoirs and the direction of heat transfer if $Q_L=100J.$

d$)$ Using the value of $Q_H$ you calculated in part c$,$ what is the efficiency or COP of this new cycle?

e$)$ What would be the $CO{P}_R$ of a Carnot cycle using the same two reservoirs? Compare your answer

to the number you calculated in part $d$ and explain why or why not the $CO{P}_R$ makes sense. Note:

Remember the Carnot refrigeration is the same as the Carnot heat engine, just in reverse.