Simple vapour compression cycle

The simple vapour compression cycle uses a refrigerant that evaporates at low pressure (absorbing heat from the cold space) and condenses at high pressure (rejecting heat to the surroundings).

          Q_H (heat rejected)
        +------------------+
   2 -->|    CONDENSER     |--> 3
        +------------------+
   ^                          |
   |                          v
 COMPRESSOR  <-- W        EXPANSION VALVE
   ^                          |
   |                          v
        +------------------+
   1 <--|    EVAPORATOR    |<-- 4
        +------------------+
          Q_L (heat absorbed)

Processes (ideal cycle)

• 1-2 Isentropic compression: dry saturated vapour at $p_e$ is compressed to superheated vapour at $p_c$.
• 2-3 Condensation at constant pressure: the vapour is desuperheated and condensed to saturated liquid, rejecting $Q_H$.
• 3-4 Throttling (isenthalpic): liquid expands in the expansion valve or capillary tube, $h_3 = h_4$; some flashes to vapour; the temperature falls to the evaporator value.
• 4-1 Evaporation at constant pressure: the wet mixture takes heat $Q_L$ from the cold space and becomes dry saturated vapour.

Diagrams

 T-s diagram                  p-h diagram
 T                            p
 |           2                |  3------------2
 |         / |                |  |           /
 |  3-----2' |                |  |         /
 |  |        |                |  |       /
 |  4--------1                |  4------1
 +-------------- s            +----------------- h

In the T-s diagram 3-2' is condensation, 2'-2 is desuperheating and 1-2 is vertical (isentropic). On the p-h diagram, lines 4-1 and 2-3 are horizontal, 3-4 is vertical (constant enthalpy) and 1-2 follows a constant-entropy line sloping upward.

Performance expressions (per kg)

$$\begin{aligned} q_L &= h_1 - h_4 = h_1 - h_3\quad\text{(refrigerating effect)}\\ w &= h_2 - h_1\quad\text{(compressor work)}\\ q_H &= h_2 - h_3\\ \text{COP} &= \frac{h_1 - h_3}{h_2 - h_1} \end{aligned}$$

Mass flow for a capacity $Q$: $\dot m = Q/(h_1 - h_4)$ and power $P = \dot m (h_2 - h_1)$.