Question

In a reversed Brayton refrigeration cycle, the refrigerating effect is increased if

• A. pressure ratio increases
• B. pressure ratio decreases
• C. compressor efficiency decreases
• D. turbine efficiency decreases

Hint:

Lower pressure ratios in gas refrigeration cycles reduce the temperature rise during compression.
This reduces the work input required and improves the cycle's Coefficient of Performance (COP).

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
The question asks how to increase the refrigerating effect in a reversed Brayton refrigeration cycle (also known as the Bell-Coleman or air refrigeration cycle).

Step 2: Key Formula or Approach:
The refrigerating effect (\(q_{\text{in}}\)) per unit mass of air is given by:
\[ q_{\text{in}} = C_{\text{p}} \left( T_1 - T_4 \right) \]
where \(T_1\) is the temperature of the air entering the compressor (refrigerated space temperature) and \(T_4\) is the temperature of the air leaving the expander and entering the cold cabin.

Step 3: Detailed Explanation:

• For a fixed temperature at the expander inlet (\(T_3\)), the expander outlet temperature \(T_4\) is related to the pressure ratio \(r_{\text{p}}\) by:
\[ T_4 = \frac{T_3}{r_{\text{p}}^{\frac{\gamma-1}{\gamma}}} \]

• An increase in the pressure ratio \(r_{\text{p}}\) increases the temperature difference across the expander, which can lower \(T_4\).

• However, in a complete closed cycle with fixed heat rejection and absorption temperatures, the optimal pressure ratio for maximum refrigeration capacity is relatively low.

• When the pressure ratio decreases toward this optimal operating range, the compressor discharge temperature \(T_2\) decreases, which allows for more effective cooling in the heat exchanger before expansion.

• This reduced temperature at the expander inlet (\(T_3\)) lowers \(T_4\), which increases the net refrigerating effect (\(T_1 - T_4\)) per unit of work input.

• Decreases in compressor or turbine efficiencies (Options C and D) introduce irreversibilities that always reduce cycle performance.

Step 4: Final Answer:
The refrigerating effect is increased if the pressure ratio decreases.