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Question #42195

Difficulty: 8/10 | 🟢 Free

The Question

A liquid-vapor mixture of total mass $m = 2 \text{ kg}$ undergoes a reversible thermodynamic cycle consisting of two isotherms at temperatures $T = 500 \text{ K}$ and $T - \Delta T = 495 \text{ K}$ , and two isochores. At the higher temperature $T$ , the cycle operates between states with vapor qualities $x_1 = 0.2$ and $x_2 = 0.8$ . The latent heat of vaporization is $L = 1500 \text{ kJ/kg}$ (assumed constant). Assuming the specific volume of the liquid phase is negligible compared to the vapor phase and $\Delta T \ll T$ , what is the net work done by the mixture during one complete cycle?

Options

A.
$18 \text{ kJ}$
B.
$30 \text{ kJ}$
C.
$9 \text{ kJ}$
D.
$1800 \text{ kJ}$

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

Cyclic Process Geometry|Specific Heat Capacity of Phase Mixtures|First Law Application

Why This Question Is Tricky

Common Mistakes

This problem exploits the misconception that standard ideal gas laws or constant specific heat capacities ( $C_p, C_v$ ) can be applied to liquid-vapor mixtures.

Students often fail to recognize that in the saturation dome, isotherms are isobars, making the $P-V$ cycle a simple rectangle.

The trap punishes those who attempt to calculate work using $W = \int P dV$ with ideal gas assumptions or who mistakenly calculate the total latent heat $mL\Delta x$ without accounting for the cyclic nature.

The correct path requires synthesizing the geometric interpretation of the cycle with the Clausius-Clapeyron relation ( $dP/dT = L/T\Delta V$ ), which elegantly eliminates the need to know the specific volume of the vapor.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Thermodynamics - Class 11 Part 2
Concept	Cyclic Process Geometry
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free