A heat pump works on the vapor compression refrigeration cycle with 0.2 kg/s of refrigerant-134a as the working fluid. The cycle is used to keep a house at 26oC while absorbing heat from the outside at 3oC. R-134a enters the compressor at 200 kPa as a saturated vapor and leaves at 900 kPa, 50oC. The refrigerant leaves the condenser as a saturated liquid. Assuming the four devices to be well-insulated:
(a) Determine the COP of the heat pump.
(b) Determine the minimum power input for this heat pump system.
To determine the COP (Coefficient of Performance) of the heat pump, we can use the equation:
COP = Qh / W
Where:
- COP is the coefficient of performance
- Qh is the heat absorbed from the outside (heat output)
- W is the work done on the system (power input)
To calculate the COP, we need to find Qh and W.
For Qh, we need to determine the amount of heat absorbed from the outside. This can be calculated using the equation:
Qh = m * h1 - m * h4
Where:
- Qh is the heat absorbed from the outside
- m is the mass flow rate of the refrigerant
- h1 is the enthalpy of the refrigerant at the compressor inlet
- h4 is the enthalpy of the refrigerant at the evaporator outlet
To find the enthalpy values, we can use a refrigerant table for R-134a at the given pressure and temperature conditions. The table provides values for enthalpy and other properties.
We also need to determine the work done on the system (power input). This can be calculated using the equation:
W = m * (h2 - h1)
Where:
- W is the work done on the system
- m is the mass flow rate of the refrigerant
- h1 is the enthalpy of the refrigerant at the compressor inlet
- h2 is the enthalpy of the refrigerant at the compressor outlet
To find the enthalpy values, we can again refer to the refrigerant table for R-134a at the given pressure and temperature conditions.
Now, let's calculate the COP and the minimum power input for this heat pump system.
(a) Determine the COP of the heat pump:
- First, find the enthalpy values:
- h1 = the enthalpy of R-134a at 200 kPa and saturation vapor temperature
- h2 = the enthalpy of R-134a at 900 kPa and 50°C
- h4 = the enthalpy of R-134a at 3°C and saturation liquid temperature
- Calculate Qh using the equation Qh = m * (h1 - h4)
- Calculate the COP using the equation COP = Qh / W
(b) Determine the minimum power input for this heat pump system:
- Calculate W using the equation W = m * (h2 - h1)
By following these steps and using the specific values provided for pressure and temperature, you can determine the COP and minimum power input for the heat pump.