Exercise: Heat Pump The aim of this exercise is to estimate the specifications of a heat pump used to provide heat for domestic applications. 1.Working Fluid Properties The working fluid is R134a (1,1,1,2-Tetrafluoroethane, formula C2H2F4, molar mass = 102 g/mol). The temperature-entropy diagram of R134a is shown page 3. 1.Estimate from the diagram the boiling temperature of evaporation of R134a at atmospheric pressure, and show this point. 2.Estimate from the diagram the temperature of the critical point of R134a, and show this point. 3.Comment on the usefulness of this fluid for heat pump applications. 2.Thermodynamical cycle We consider a heat pump operating along the usual cycle: •A ⇒ B: The working fluid vaporizes at the contact of the cold source (Tcold=-10°C) until the last liquid droplet disappears. •B⇒C: The working fluid is compressed with a given compression ratio r. This compression will be considered as adiabatic and isentropic. CC': The working fluid cools down at constant pressure until it starts liquefying. •C' ⇒ D: The working fluid liquefies at the contact of the hot source (Thot-40°C), until the last gas disappears. •D⇒ A: The working fluid is decompressed through throttling. This process is iso-enthalpic. Calculations will be performed per unit of mass of the working fluid. bubble 1. At which pressure should the fluid be brought to vaporize by draining heat from the cold source? Locate point B on the diagram. 2. What is the compression ratio of step 2? Locate points C, C' and D on the diagram. 3. What are the advantage and drawbacks of performing the B ⇒ C ⇒ C' compression / decompression sequence, rather than compress directly B⇒C' ? 3.Heat Pump We now evaluate the COP of the device working as a heat pump. 1.Assuming the working fluid behaves like an ideal gas, express the temperature at the end of compression Tc as a function of the compression ratio, the temperature of the cold source and the adiabatic coefficient y of R134a. 2. Evaluate from the diagram the temperature Tc. Show that the effective adiabatic coefficient is y=1.16 3. Estimate the amount of work provided by the compressor to the working fluid. 4. Estimate the amount of heat provided to the hot source during the cooling step C ⇒ C’ 5. Estimate the amount of heat provided to the hot source during the liquefaction step C' ⇒ D 6. Deduce the COP of the device used as a heat pump. Comment your result. 150 Isenthalpic (iso-H) 125 Isobaric (iso-P) Isotitle (constant vapour fraction) 100 15 75 T in °C 50 25 0 -25 -50 0.8 1.0 bar 0.5 bar- 2.0 bar 200.0% 1.0 225.0 100.0 bar 700.0 bar 500.0 bar 200.0 bar 5.0 bar! -0.3. 10.0 bar- 250.0 20.0 bary 275.0 50.0 bar.. 325.0 40- 90 300.0 1.2 1.4 kl sin kgK 1.6 350.0 1.8 2.0