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?

To understand the effect of replacing the throttling process with an isentropic expansion process in an ideal vapour compression refrigeration cycle (VCRC), let us analyze the changes in the cycle's performance parameters.

The Coefficient of Performance (COP) of a refrigeration cycle is defined as the ratio of the desired refrigerating effect to the net work input:
$\mathrm{COP}=\frac{Q_{\mathrm{in}}}{W_{\mathrm{net}}}$
where:
$Q_{\mathrm{in}}$ is the refrigerating effect (heat absorbed in the evaporator), and
$W_{\mathrm{net}}$ is the net work input to the cycle.

In the standard VCRC:
1. The expansion process (from the condenser pressure to the evaporator pressure) is a throttling process, which is isenthalpic (constant enthalpy). Throttling is highly irreversible and results in a loss of potential refrigerating effect because the refrigerant enters the evaporator with a higher enthalpy compared to an isentropic process.
2. No work is recovered during throttling, so the net work input is equal to the compressor work:
$W_{\mathrm{net}}=W_{\mathrm{compressor}}$

When the throttling process is replaced by an isentropic expansion process (using an expander or turbine):
1. Increase in Refrigerating Effect: Because the isentropic expansion process is reversible and adiabatic, the enthalpy of the refrigerant drops more than it does during isenthalpic throttling. Thus, the refrigerant enters the evaporator at a lower enthalpy state, which increases the heat absorbing capacity (refrigerating effect, $Q_{\mathrm{in}}$) in the evaporator.
2. Decrease in Net Work Input: The isentropic expansion process produces some work output ($W_{\mathrm{expander}}$). This work output can be utilized to help run the compressor, thereby reducing the net external work required by the cycle:
$W_{\mathrm{net,\; modified}}=W_{\mathrm{compressor}}-W_{\mathrm{expander}}$
Therefore, the net work input decreases.

Since the refrigerating effect ($Q_{\mathrm{in}}$) increases and the net work input ($W_{\mathrm{net}}$) decreases, the Coefficient of Performance (COP) of the modified cycle must increase:
${\mathrm{COP}}_{\mathrm{modified}}=\frac{Q_{\mathrm{in,\; modified}}}{W_{\mathrm{net,\; modified}}}>{\mathrm{COP}}_{\mathrm{original}}$

Thus, the Coefficient of performance is higher than that of the original cycle.