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Question #42558

Difficulty: 8/10 | 🟢 Free

The Question

In a steady-state cryogenic refrigerator, the refrigerant enters the evaporator as a liquid with specific enthalpy $h_1 = 150 \text{ kJ kg}^{-1}$ at negligible velocity. It absorbs heat from the cold space and exits the evaporator through a converging nozzle as a saturated vapor with specific enthalpy $h_2 = 310 \text{ kJ kg}^{-1}$ and a velocity $v = 200 \text{ m s}^{-1}$ . The high-velocity vapor directly enters an adiabatic compressor, where it is compressed and decelerated to a final state with specific enthalpy $h_3 = 370 \text{ kJ kg}^{-1}$ at negligible velocity. What is the Coefficient of Performance (COP) of this refrigerator?

Options

A.
$4.5$
B.
$4.0$
C.
$3.0$
D.
$2.67$

Check Your Answer

Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Intuition_Breaker

Train your brain to resist "obvious" answers that are designed to deceive your intuition.

Concepts Behind This Question

Refrigerator Coefficient of Performance|Bernoulli’s Energy Balance|Latent Heat and Volume Change

Why This Question Is Tricky

Common Mistakes

This question tests the application of the First Law of Thermodynamics for open systems (Steady Flow Energy Equation) by coupling enthalpy changes with macroscopic kinetic energy.

A common 'Lethal Collision' for students is treating the compressor and evaporator purely algebraically using static enthalpies ( $q_{in} = h_2 - h_1$ and $w_{in} = h_3 - h_2$ ), completely ignoring the Bernoulli-type kinetic energy terms ( $v^2/2$ ).

By forcing a high-velocity nozzle transition between the evaporator and compressor, the problem requires students to recognize that the kinetic energy gained in the evaporator contributes to the total cooling effect, and its subsequent recovery in the compressor reduces the required mechanical work.

Failing to account for the $20 \text{ kJ kg}^{-1}$ kinetic energy term leads to incorrect COP values of 2.67, 3.0, or 4.0.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Thermodynamics - Class 11 Part 2
Concept	Refrigerator Coefficient of Performance
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free