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Question #42524

Difficulty: 8/10 | 🟢 Free

The Question

A mass $m$ of a liquid boils and transforms into vapor at a constant temperature $T$ and pressure $P$ . The latent heat of vaporization of the liquid is $L$ . If the slope of the liquid-vapor phase boundary in the pressure-temperature ( $P-T$ ) diagram at this state is given by $\frac{dP}{dT}$ , which of the following expressions correctly represents the change in internal energy ( $\Delta U$ ) of the system during this complete phase transition?

Options

A.
$mL \left( 1 - \frac{P}{T} \frac{dT}{dP} \right)$
B.
$mL$
C.
$mL \left( 1 + \frac{P}{T} \frac{dT}{dP} \right)$
D.
$mL \left( \frac{P}{T} \frac{dT}{dP} \right)$

Check Your Answer

Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Multi-Concept_Bridge

Master problems that require linking physics and math concepts to solve complex competitive questions.

Concepts Behind This Question

Latent Heat and Volume Change|Internal Energy Dependency|Integration

Why This Question Is Tricky

Common Mistakes

This question tests the fundamental understanding of the First Law of Thermodynamics during phase transitions, specifically targeting the misconception that latent heat solely contributes to internal energy ( $\Delta U = mL$ ).

Students often forget that latent heat represents an enthalpy change ( $\Delta H$ ), and the non-negligible volume expansion during boiling means significant work is done ( $P\Delta V$ ).

By forcing the use of the Clausius-Clapeyron equation to find the volume change, the problem elegantly bridges phase equilibrium and the First Law, trapping students who either rote-memorize $\Delta U = mL$ or fail to connect the $P-T$ slope to mechanical work.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Thermal Properties of Matter - Class 11 Part 2
Concept	Latent Heat and Volume Change
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free