Question

Problem 2 (30 pts): Consider a two-stage vapor-compression refrigeration system operating between the pressure limits of 1.5 MPa and 150 kPa with refrigerant-134a as the working fluid. The refrigerant leaves the condenser as a saturated liquid and is throttled to a flash chamber operating at 0.45 MPa. The mass flow rate of the refrigerant through the low pressure compressor is 0.15 kg/s. Assuming the refrigerant leaves the evaporator as a saturated vapor, determine (a) the mass flow rate of the refrigerant through the high-pressure compressor, (b) the rate of heat removal from the refrigerated space, and (c) the COP of this refrigerator. USE THE P-H CHART. Pla OH Expanse O:

please answer all parts and show all work. Please include P-h chart work as welll

Answer 1

A two-stage cascade refrigeration system is considered. Each stage operates on the ideal vapor-compression cycle with refrigerant-134a as the working fluid. The mass flow rate of refrigerant through the lower cycle, the rate of heat removal from the refrigerated space, the power input to the compressor, and the COP of this cascade refrigerator are to be determined.

Assumptions

1 Steady operating conditions exist.

2 Kinetic and potential energy changes are negligible.

3 The flash chamber is adiabatic.

QH Condenser 5 Expansion valve High-press. Compressor 4 6 9 Flash chamber 3 2 Expansion valve Low-press. Compressor LE 8 Evaporator Q

TA 1.5 MPa 0.45 MPa A 0.15 MPa 6 39 B 8 9.

Analysis

(a) The properties are to be obtained from the refrigerant tables (Tables A-11 through A-13 of Yunus Cengel Textbook of Thermodynamics):

using R134a pah chart 1 Table hi hg @ 0.15 mpa 240.14 kJ/kg Si = Sg @ 0:15. MPa = 0.9 4.323. KI/kg. ha 262.7 KJ/kg @ P2=0.45 MPa and 52 = S, ha= hg @ 0.45 MPa 254.53 KI/kg hoa hf @ 1.5MPa = 131.58 KJ KJ/kg ho=h5 131.58 kJ/kg (Isenthalpic expansion) hq hf@ 0.45MPa = 68.81 kJ/kg h8 = h7 = 68.81 kJ/kg Cisen talpic expansion) ho = 131.58 kJ/kg } a 6 0.33 Po 0.45 MPa a] The mass flow rate of refrigerant through the high pressure.compressor is determined from the mass on the flash chamber balance m m7 0.15 0.2239 kg/s 1-26 10.33 ñ 0.2239 kg/s. img=m-my = 0.2239 -0.15 = 0.0739 kg/s -] at state 9 is Enthalpy an energy inha determined from the mixing chamber on balance ny hat - na ha 0.2239 x hg. = 0.15 x 262.7 t 0.07 39 x 257.53 hg = 261 kJ/kg Now At Pg 20,45 MPa } S9 = 0-937 kJ/kg 26165/kg hg. h4 = 286.3 kJ/kg @ P4 = 1.5 MPa and S4=8g Rate of heat removal.com from the refrigerated space Q = my chinho) å. 0.15% (240.14 – 68.81) ÅL = 25.7kW c] Cop of system Power input (Win): Win = my cha-ho tin Chu-hg) = 0.15 x (262.7 – 240-14) 0.2239 x C 28 6.3 - 261) Win= 9.05 KW cop= QL Win 25.7 9.05 COD= 2.84