Consider an ideal vapour compression refrigeration cycle. If the throttling process is Q.2 replaced by an isentropic expansion process, keeping all the other processes unchanged, which one of the following statements is true for the modified cycle?

The correct option is: Coefficient of performance is higher than that of the original cycle.

To understand why this statement is true, let us analyze the effects of replacing the throttling process with an isentropic expansion process in an ideal vapour compression refrigeration cycle (VCRC).

The Coefficient of Performance (COP) of a refrigeration cycle is defined as the ratio of the desired refrigerating effect to the net work input required by the cycle:

$$\text{COP}=\frac{Q_{\text{in}}}{W_{\text{net}}}=\frac{q_e}{w_c-w_e}$$

where:
• $q_e$ is the specific refrigerating effect (heat absorbed in the evaporator),
• $w_c$ is the work input to the compressor, and
• $w_e$ is the work output recovered from the expansion process (which is zero in a throttling process).

Let us compare the two scenarios:

1. Original Cycle (with Throttling):
Throttling is an irreversible, isenthalpic process (constant enthalpy, $h_3=h_4$). No work is produced during throttling ($w_e=0$). The refrigerating effect is given by:
$$q_{e,\text{original}}=h_1-h_4=h_1-h_3$$
The net work input required is simply the compressor work:
$$W_{\text{net},\text{original}}=w_c=h_2-h_1$$

2. Modified Cycle (with Isentropic Expansion):
When throttling is replaced by an isentropic expansion process (from state 3 to a new state 4'), the process is reversible and adiabatic, meaning entropy remains constant ($s_3=s_{4\text{'}}$). On a Temperature-Entropy (T-s) or Pressure-Enthalpy (p-h) diagram, thisisentropic expansion line lies to the left of the isenthalpic throttling line, resulting in a lower enthalpy at the evaporator inlet:
$$h_{4\text{'}}<h_4$$
This reduction in enthalpy leads to two major benefits:
• Increase in Refrigerating Effect: The new refrigerating effect becomes:
$$q_{e,\text{modified}}=h_1-h_{4\text{'}}$$
Since $h_{4\text{'}}<h_4$, the refrigerating effect increases ($q_{e,\text{modified}}>q_{e,\text{original}}$).
• Decrease in Net Work Input: The expander produces positive work output ($w_e=h_3-h_{4\text{'}}>0$) which can be utilized to run the compressor. Thus, the net work input decreases:
$$W_{\text{net},\text{modified}}=w_c-w_e<w_c$$

Conclusion:
Since the refrigerating effect (numerator) increases and the net work input (denominator) decreases, the Coefficient of Performance (COP) of the modified cycle increases significantly compared to the original cycle.