A reversible heat engine runs between high temperature T1 and low temperature T2. The work output of this heat engine is used to run a reversible refrigeration cycle absorbing heat at temperature T3 and rejecting at temperature T2. What is the COP of the combined system?
(a) $\left ( \frac{T_{1}-T_{2}}{T_{1}} \right )\left ( \frac{T_{3}}{T_{2}-T_{T_{3}}} \right )$
(b) $\left ( \frac{T_{2}}{T_{1}-T_{2}} \right )\left ( \frac{T_{2}-T_{3}}{T_{3}} \right )$
(c) $\left ( \frac{T_{1}}{T_{1}-T_{2}} \right )\left ( \frac{T_{3}}{T_{2}-T_{3}} \right )$
(d) $\left ( \frac{T_{3}}{T_{1}-T_{3}} \right )\left ( \frac{T_{1}}{T_{2}-T_{1}} \right )$