The vapour compression refrigerator employs the following cycle

General
1

the vapour compression refrigerator employs the following cycle

2

The vapour compression refrigerator employs the following cycle

Answer:
The vapour compression refrigeration (VCR) cycle is a widely used method for refrigeration, air conditioning, and heat pumps. This cycle involves the following main components: evaporator, compressor, condenser, and expansion valve. It operates based on the principles of thermodynamics and phase changes of the refrigerant. Below, each step of the VCR cycle is explained in detail:

1. Evaporation:

  • Process: The refrigerant enters the evaporator as a low-pressure liquid and evaporates by absorbing heat from the refrigerated space. This phase change from liquid to vapor removes heat from the space to be cooled.

  • Thermodynamics: This is an isothermal process where the refrigerant absorbs latent heat of vaporization. The refrigerant leaves the evaporator as a low-pressure, low-temperature vapor.

    \Delta Q = m \cdot h_{\text{evaporation}}

2. Compression:

  • Process: The low-pressure vapor from the evaporator is drawn into the compressor, where it is compressed to a high-pressure, high-temperature vapor.

  • Thermodynamics: This is an adiabatic compression process, wherein the pressure and temperature of the refrigerant increase without any heat exchange with the surroundings. Work is done on the refrigerant by the compressor.

    W_{\text{comp}} = m \cdot c_p \cdot \Delta T_{\text{comp}}

3. Condensation:

  • Process: The high-pressure, high-temperature vapor enters the condenser, where it releases heat to the surroundings and condenses into a high-pressure liquid.

  • Thermodynamics: This is an isothermal process where the refrigerant releases its latent heat of condensation to the surrounding. The refrigerant leaves the condenser as a high-pressure, medium-temperature liquid.

    \Delta Q = m \cdot h_{\text{condensation}}

4. Expansion:

  • Process: The high-pressure liquid refrigerant passes through the expansion valve (or throttling valve), where it undergoes a rapid pressure drop, leading to partial vaporization (flash evaporation).

  • Thermodynamics: This is an adiabatic process where the temperature and pressure of the refrigerant drop significantly. The refrigerant becomes a low-pressure mixture of liquid and vapor.

    \text{h}_1 = \text{h}_2 \quad (\text{enthalpy remains constant})

Cycle Illustration:
Here’s a simplified diagram illustrating the components and processes involved in the VCR cycle:

  Low-Pressure Vapor ->   | Compressor | -> High-Pressure Vapor
       ^                                               |
       |                                               v
  Evaporator <- | Expansion Valve | <- Condenser
  Low-Pressure Liquid                                   High-Pressure Liquid

Steps and Thermodynamic Processes:

  1. Evaporation (Process 1-2):

    • The refrigerant absorbs heat from the refrigerated space (Qin) and evaporates.

    • T-s diagram: This is an isothermal process at the evaporator temperature.

      $$ t_{\text{evap}} = \text{constant} $$

  2. Compression (Process 2-3):

    • The refrigerant is compressed to a high-pressure state (Work input W).

    • T-s diagram: This represents an adiabatic process, with a vertical line indicating no heat exchange.

      $$ s_{\text{in}} = s_{\text{out}} $$

  3. Condensation (Process 3-4):

    • The refrigerant releases heat (Qout) to the surroundings and condenses into a liquid state.

    • T-s diagram: This is an isothermal process at the condenser temperature.

      $$ t_{\text{cond}} = \text{constant} $$

  4. Expansion (Process 4-1):

    • The refrigerant undergoes an expansion, reducing pressure and temperature.

    • T-s diagram: An adiabatic process, often represented as a horizontal line due to constant enthalpy.

      $$ h_1 = h_2 $$

The vapour compression refrigeration cycle is thus a sequence of thermodynamic processes that utilize phase changes and pressure differences to achieve efficient cooling. This cycle is foundational in modern refrigeration and air conditioning systems. The efficiency of this cycle can be evaluated using the Coefficient of Performance (COP) which is a measure of the system’s performance.

Coefficient of Performance (COP):

COP = \frac{Q_{in}}{W_{comp}}

The COP is a crucial metric, as a higher COP indicates a more efficient refrigeration cycle.