Problem $4$:

As shown in the figure, a reversible power cycle $R$ and an irreversible power cycle I operate between the same hot and cold reservoirs. Cycle I has a thermal efficiency equal to one$-$third of the thermal efficiency of cycle R$.$

If each cycle develops the same net amount of work, determine:

a$)$ Which cycle receives greater energy by heat transfer from the hot reservoir,

b$)$ Which cycle discharges greater energy by heat transfer to the cold reservoir.

Problem $5$:

Two reversible power cycles operate between hot and cold reservoirs at temperature $T_H$ and $T_C$ respectively.

a$)$ If one is a power cycle and the other is a heat pump cycle, what is the relation $($write an expression$)$ between the coefficient of performance of the heat pump cycle and the thermal efficiency of the power cycle?

b$)$ If one is refrigeration cycle and the other is a heat pump cycle, what is the relation $($write an expression$)$ between their coefficients of performance?

Show where you found any numbers from tables in both questions