Question

Determine the nature of the following cycle (reversible, irreversible, or impossible): a refrigeration cycle draws heat from a cold reservoir at 250 K and rejects 950 KJ to a hot reservoir at 300 K while receiving 70 kJ of work to operate. Draw a schematic of the cycle clearly indicating the hot and cold reservoir and the direction of heat and work transfers. (10 pts.)

Answer 1

Answer:

Impossible.

Explanation:

The ideal Coefficient of Performance is:

$COP_{i} = \frac{250\,K}{300\,K-250\,K}$

$COP_{i} = 5$

The real Coefficient of Performance is:

$COP_{r} = \frac{950\,kJ-70\,kJ}{70\,kJ}$

$COP_{r} = 12.571$

Which leads to an absurds, since the real Coefficient of Performance must be equal to or lesser than ideal Coefficient of Performance. Then, the cycle is impossible, since it violates the Second Law of Thermodynamics.