Question

A two-stage compression refrigeration system with an adiabatic liquid-vapor separation unit uses refrigerant-134a as working fluid. The system operates the evaporator at 0.4 MPa, the condenser at 1.6 MPa, and the separator at 0.8 MPa. The compressors use 25 kW of power. Given that the refrigerant is saturated liquid at the inlet of each expansion valve and saturated vapor at the inlet of each compressor, and the compressors are isentropic: (0) show the process on a T-s diagram; ) calculate the rate of cooling provided by the evaporator, the COP of the heat pump: and full) determine the COP of this cycle.

Answer 1

You probably know, how to get enthalpy at all the points right?

I still shown taht in short on first written page.

2 Condenser Compressor 3 Separator Expansion valve 8 + Compressor 4 5 Expansion valve 7 Evaporator 6

The below image solves the section i)

T 16 bar 3 8 8 bar 5 4 4 bar 6 7 QL S

I am not going to show basics like pressure conversion of Mpa to bar and celcius to kelvin to keep solution clear. Its basics. If you have any difficulty regarding such things let me know in the comment

from refrigeration table R134a coe get P, = 8 bar sat vapour } his hg = 415 kJ /kg P2 = 16 bar S2=5, (at & bar) = 1.7144 kJ/kg k (Tsup S₂ = Sgt Cppln [tsat STsup 1.7144 = 1.7042 + (0.92) en 57.91+273 = 334.6k= 61.6 °C Tsup ha = hg & Co (Tsup - Tsat) = 426.27 + (0.92) 3346 (61.6 - 57.91) hz = 429.66 kJ/kg Pa = 16 bar sat. liquid hz=hf = 284. 11 kJ/kg = hu (throttling hz=hy Ps = 8 bar) ho=he = 243.58 kJ/kg Sat. liquid hs = ho (Throttling) = 4 bar Pz Sat. vapour S } ha a hg = 403.8 kJ / kg So = Sg + Corle [Trup P8 8 bar . So = S 34.15°C 57 1.7229 = 1.7144 + (0.92) en (I suppo + 273 = 1.7229 kJ / kg k Toup - 307. Isk = ho = hq + Cav (Tsop - Tsat) = 415.58 + (0.92) (34.15 – 31.33) hq = 418. 17 kJ/kg

On below image we used energy balace to calculate mass flow rate

$1594630426288_IMG_20200713_141632.png$

two answers of section ii) and answer of section III) are on below page

$1594630450390_IMG_20200713_141653.png$

Hope you are satisfied with the solution

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