In air-conditioning system operating on the reversed Carnot cycle is required to transfer heat from a house at a rate of 750 kJ/min to maintain its temperature at 24°C. If the outdoor air temperature is 35°C, determine the power required to operate this air-conditioning system. The power required to operate this air-conditioner system.

Answer

The required Power 0.46watt

Explanation:

In the reverse Carnot cycle, work is done to extract heat from one system and expel it into another via four processes, two isothermal and two isentropic.

Given data

Given that the heat transfer from the house

Q=750kj/min

Temperature of the house T1=24°C to Kelvin 24+273=297k

Outdoor temperature T2=35°c

To Kelvin =35+273=308k

We are assuming a steady state operation

Hence the coefficient of performance c.o.p for a reversed Carnot cycle operating between two temperatures is

C.O.P= 1/(T2/T1) - 1

=1(308/297)-1

=1/1.037-1

=1/0.037

COP=27.02

The expression for net work done

Is given as

Wnet=Quantity of heat transfer/COP

Wnet=750/27.02

Work =27.75j/min

To get the power let's us divide the work done by 60min

Power =27.75/60

Power =0.46watt

6 cos 34, 6 sin 34 trig