### Understanding Heat Pump Systems**Concept**: A heat pump with refrigerant R-134a as the working fluid is used to maintain a steady temperature by absorbing heat. Here's how it works in this specific example:1. **Evaporator**: The system uses geothermal water entering at 50°C into the evaporator. The refrigerant absorbs heat at 50°C, resulting in a change of phase (vaporization).2. **Mass Flow Rate and Quality**: The refrigerant enters this part at a rate of 0.05 kg/s and leaves at 20°C with a quality (x) of 0.92, meaning 92% of the refrigerant is vapor.3. **Compressor**: The refrigerant vapor then moves to the compressor. The compressor consumes 2.3 kW of work and compresses the refrigerant up to a pressure of 1.4 MPa.4. **Condenser**: After compression, the refrigerant flows into the condenser. This process allows the refrigerant to release absorbed heat to the surroundings. The heat is released at the same entropy as the inlet, with no change in entropy.5. **Expansion Valve**: The cooled refrigerant passes through an expansion valve where it is expanded, and the cycle repeats. **Tasks**:- Determine the degree of subcooling at point 4 (just after the condenser).- Calculate the coefficient of performance (COP) of the heat pump.- Evaluate the theoretical minimum power input required for the same heating load.### Diagram DetailsThe diagram shows a closed-loop system consisting of four main components connected by piping:- **Evaporator (left side)**: Geothermal water enters and exits, transferring its heat to the refrigerant.- **Compressor (bottom)**: Shown with an arrow labeled as work input \( W_{in} \).- **Condenser (top right)**: Tubing indicates the flow of heat rejection \( Q_H \).- **Expansion Valve (top)**: Positioned before the evaporator to reduce pressure and temperature of the refrigerant.The refrigerant flow is depicted with arrows and labeled states to show the transition of states from saturated vapor at the evaporator to the subcooled liquid state as it goes back to the compressor. The mass flow rate (\( \dot{m} \)), pressure, temperature, and quality at various points are indicated to understand the thermodynamic

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2. 11-43 A heat pump with refrigerant-134a as the working fluid is used to keep a space at 25°C by absorbing heat from geothermal water that enters the evaporator at 50°C at a rate of 0.065 kg/s and leaves at 40°C. The refrigerant enters the evaporator at 20°C with a quality of 23 percent and leaves at the inlet pressure as saturated vapor. The refrigerant loses 300 W of heat to the surroundings as it flows through the compressor and the refrigerant leaves the compressor atl.4 MPa at the same entropy as the inlet. Determine (a) the degrees of subcooling of the refrigerant in the condenser, (b) the mass flow rate of the refrigerant, (c) the heating load and the COP of the heat pump, and (d) the theoretical mini- mum power input to the compressor for the same heating load. 1.4 MPa 2- 52= 51 Condenser Expansion valve Compressor Evaporator sat. vapor 20°C x= 0.23 40°C Water 50°C

2. 11-43 A heat pump with refrigerant-134a as the working fluid is used to keep a space at 25°C by absorbing heat from geothermal water that enters the evaporator at 50°C at a rate of 0.065 kg/s and leaves at 40°C. The refrigerant enters the evaporator at 20°C with a quality of 23 percent and leaves at the inlet pressure as saturated vapor. The refrigerant loses 300 W of heat to the surroundings as it flows through the compressor and the refrigerant leaves the compressor atl.4 MPa at the same entropy as the inlet. Determine (a) the degrees of subcooling of the refrigerant in the condenser, (b) the mass flow rate of the refrigerant, (c) the heating load and the COP of the heat pump, and (d) the theoretical mini- mum power input to the compressor for the same heating load. 1.4 MPa 2- 52= 51 Condenser Expansion valve Compressor Evaporator sat. vapor 20°C x= 0.23 40°C Water 50°C

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

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Question

### Understanding Heat Pump Systems

**Concept**: A heat pump with refrigerant R-134a as the working fluid is used to maintain a steady temperature by absorbing heat. Here's how it works in this specific example:

1. **Evaporator**: The system uses geothermal water entering at 50°C into the evaporator. The refrigerant absorbs heat at 50°C, resulting in a change of phase (vaporization).

2. **Mass Flow Rate and Quality**: The refrigerant enters this part at a rate of 0.05 kg/s and leaves at 20°C with a quality (x) of 0.92, meaning 92% of the refrigerant is vapor.

3. **Compressor**: The refrigerant vapor then moves to the compressor. The compressor consumes 2.3 kW of work and compresses the refrigerant up to a pressure of 1.4 MPa.

4. **Condenser**: After compression, the refrigerant flows into the condenser. This process allows the refrigerant to release absorbed heat to the surroundings. The heat is released at the same entropy as the inlet, with no change in entropy.

5. **Expansion Valve**: The cooled refrigerant passes through an expansion valve where it is expanded, and the cycle repeats.

**Tasks**:
- Determine the degree of subcooling at point 4 (just after the condenser).
- Calculate the coefficient of performance (COP) of the heat pump.
- Evaluate the theoretical minimum power input required for the same heating load.

### Diagram Details

The diagram shows a closed-loop system consisting of four main components connected by piping:

- **Evaporator (left side)**: Geothermal water enters and exits, transferring its heat to the refrigerant.
- **Compressor (bottom)**: Shown with an arrow labeled as work input \( W_{in} \).
- **Condenser (top right)**: Tubing indicates the flow of heat rejection \( Q_H \).
- **Expansion Valve (top)**: Positioned before the evaporator to reduce pressure and temperature of the refrigerant.

The refrigerant flow is depicted with arrows and labeled states to show the transition of states from saturated vapor at the evaporator to the subcooled liquid state as it goes back to the compressor. The mass flow rate (\( \dot{m} \)), pressure, temperature, and quality at various points are indicated to understand the thermodynamic

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