question_answer

         A reversible heat engine runs between high temperature \[{{T}_{1}}\] and low temperature \[{{T}_{2}}.\] the work output of this heat engine is used to run a reversible refrigeration cycle absorbing heat at temperature \[{{T}_{3}}\] and rejecting at temperature \[{{T}_{2}}.\]what is the COP of the combined system?

A) \[\left( \frac{{{T}_{1}}-{{T}_{2}}}{{{T}_{1}}} \right)\,\,\left( \frac{{{T}_{3}}}{{{T}_{2}}-{{T}_{3}}} \right)\]

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) \[\left( \frac{{{T}_{3}}}{{{T}_{1}}-{{T}_{3}}} \right)\,\,\left( \frac{{{T}_{1}}}{{{T}_{2}}-{{T}_{1}}} \right)\]