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Thermal power required to heat the building: 12.1 kW at condensing temperature tc = 44.3 deg C

For the evaporator: vaporizing temperature tv = -7 deg C

Subcooling temperature for the heat pump Δ tsc = 5 deg C

adiabatic coefficient: k = 1.16

vaporising pressure: pv =t(tv) =paspiration =4bar

condensing pressure: pc = t(tc) = pdischarge =17bar

vapor density: ρv=17.0 kg/m

^{3}

specific volume for aspiration vaspiration = 1/ρv = 1/17kg/m

^{3}= 0.058823529 m

^{3}/kg

internal compressor efficiency: ηi=0.84

h1= hv(tv) = 402.56 kJ/kg

h3 =hl(tsc,pc) =248.6 kJ/kg

Now I tried finding out the following:

a)Thermal power Q0 at the evaporator

b)Compressor power

c)efficiency of the heat pump (both COP and refrigeration cycle efficiency ε )

a)Q0=q0*mrf, where q0 = specific heat load, and mrf=mass floware for the refrigerant

q0 = h1-h4 = h1-h3; because h3=h4

so q0 = 402.56 kJ/kg - 248.6 kJ/kg => q0 = 153.96kJ/kg

compressor work: compressor_work = (k/((k-1)*ηi))*paspiration*vaspiration*((pdischarge/paspiration)^((k-1)/k)-1)*100

compressor_work = 44.85735668 kJ/kg

enthaply in the 2nd point: h2 = h1+compressor_work = 402.56 kJ/kg+44.85735668 kJ/kg

h2 = 447.4173567 kJ/kg

specific heat load at the condenser: qc = h2-h3 = 447.4173567 kJ/kg - 248.6 kJ/kg

qc =198.8173567 kJ/kg

so: mrf = Qc/qc = 12.1 kW/198.8173567 kJ/kg

mrf = 0.060859878 kg/s (refrigerant mass flowrate)

Thermal power Q0 at the evaporator: Q0=q0*mrf

Q0 = 153.96kJ/kg*0.060859878 kg/s

Q0 = 9.369986761 kW

b)Compressor_power = (mass_flowrate_refrigerant * compressor_work) / (ηmotor*ηelectrical)

Problem arises here because I was given just the internal efficiency ηi=0.84, but the formula uses the efficiency of the motor ηmotor and the electrical efficiency ηelectrical...so how can I calculate this? (as I don't have the ηmotor*ηelectrical), I don't want to guess though...

c)COP =qc/work_compressor = 198.8173567 kJ/kg / 44.85735668 kJ/kg

COP = 4.432

ε = heat load evaporator/work done = COP - 1 = 3.432

What do you think of the calculations, do they make any sense? I'd really appreciate a peer review.

My actual question is, how can I calculate the compressor power at b) as I don't have those 2 efficiencies (ηmotor and ηelectrical), but just the ηi which is the internal efficiency of the compressor?