Estimation of Coefficient of performance of Carnot refrigeration cycle:

If Carnot refrigeration cycle absorbs heat at 270 K & rejects heat at 300 K.

(1) Estimate the coefficient of performance of refrigeration cycle.

(2) If the cycle is absorbing 1130 kJ/min at 270 K, Determined how many kJ of work is needed per second.

(3) If the Carnot heat pump operates among the similar temperatures like the above refrigeration cycle, determine coefficient of performance.

(4) How many kJ/min shall the heat pump deliver at 300 K if this absorbs 1130 kJ/min at 270 K.

Solution

It is given that : T₁ = 270 K; T₂ = 300 K

(1) Estimation of Coefficient of performance of Carnot refrigeration cycle

We already know that coefficient of performance of Carnot refrigeration cycle,

       Ans.

 (2) Work needed per second

Assume            WR = Work required per second

Heat absorbed at 270 K (that is. T₁),

Q₁ = ll30 kJ/min= 18.83 kJ/s

We already know that (C.O.P)R : Q₁/W_R

                      WR = 2.1 kJ/s    Ans.

(3) Now to estimate Coefficient of performance of Carnot heat pump

Already we know that coefficient of performance of a Carnot heat pump,

 (4) Heat delivered through heat pump at 300 K

Assume Q₂ = Heat delivered through heat pump at 300 K.

Heat absorbed at 270 K (that means. T₁),

 Q₁ = 1130 kJ/min  (Given)

As we know that (C.O.P.)p =

 Q₂ = 1256 kJ/min                         Ans.