Question

The thermal efficiency of a power cycle operating in a reversible manner is found to be 50%. Assuming that the same 2 thermal reservoirs are now used to power a reversible refrigeration system and then a reversible heat pump, determine the Coefficient of Performance of these two systems.

Answer 1

Step-by-step explanation:

The thermal efficiency of a Power cycle
`\eta = (Q_H -Q_c)/(Q_H)`

where;

`\eta = 50\% = 0.5`

`Q_H = Heat \ flow \ from \ higher \ temperature`

`Q_c = Heat \ flow \ from \ lower \ temperature`

`0.5 = (Q_H -Q_c)/(Q_H)`

`0.5 Q_H = Q_H - Q_c` --- (1)

`Q_c = 0.5 Q_H` ---- (2)

The coefficient of performance is:

`COP_R = (Q_c)/(Q_H -Q_c)`

let replace the value of
`Q_c = 0.5 Q_H` in the above equation then;

`COP_R = (0.5Q_H)/(Q_H -0.5 Q_H)`

`COP_R = (0.5Q_H)/(0.5 Q_H)`

`COP_R = 1`

The

On the other hand, the heat pump

`COP_(HP) = (Q_H)/(Q_H -Q_c)`

By replacing equation (1) into the above equation; we have:

`COP_(HP) = (Q_H)/(0.5Q_(H))`

`COP_(HP) = (1)/(0.5)`

`COP_(HP) =2`

t