4 ) Problem (4A) Consider two Carnot heat engines operating in series. The first

Question

4 ) Problem (4A) Consider two Carnot heat engines operating in series. The first engine receives heat from the source at TH =1727?C and rejects the waste heat to another sink at temperature T. The second engine receives this heat rejected by the first one, converts some of it to work, and rejects the rest to a reservoir at TL =27?C. If the thermal efficiencies of both engines are the same, determine the temperature of the intermediate medium, T (in ?C ) between the two engines.


Problem (4B) Refrigerant-134a enters the evaporator coils at 120 kPa with a quality 20% and leaves at -20?C as a saturated liquid. If the compressor consumes 450 J/s of power and the COP of the refrigerator is 1.2. Determine
(a) the COP of the mass flow rate(in kg/s) and
(b) the rate(in W) of heat rejected to the kitchen air.

Explanation / Answer

4A) So, for a carnot heat engine we know that efficiency can be deduced as:
n = 1 - TL/TH

We do not know the actual efficiency of either engine, but we know that n is equal for both, and that TL of the first engine will be equal to TH of the second engine. So for the first engine:

n = 1 - TL(1)/2000 K

And for the second engine efficiency we can replace the TH with TL(1)

n = 1 - TL/TL(1)

The TL(1) Can be rewritten as TM for the middle source temp, and TL can be subbed in:

n = 1 - 300 K/TM

Now we substitute the fefficiency of the first engine in with the second:

1 - TM/2000K = 1 - 300 K/TM

TM = 774.6 K

4B) I am not sure exactly what part A is asking. The refridgerator as a whole has a COP, but I have not heard of just the mass flow rate having its own COP.

For B part, we can use the following COP equation:

COPR = QL/W

1.2 = QL/450

QL = 540 J/s

COPR = QL/(QH- QL)

1.2 = 540/(QH - 540)

QH = 990 J/s

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