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Question #42521

Difficulty: 8/10 | 🟢 Free

The Question

A perfectly insulated cylinder is fitted with a movable, frictionless piston. The cylinder contains $n$ moles of an ideal gas and a mass $m$ of ice. Initially, the system is in thermal equilibrium at temperature $T_0$ (the melting point of ice) and the gas pressure is $P_0$ . The piston is slowly pushed inward by an external force until all the ice just melts. The gas and the ice-water mixture remain in thermal equilibrium throughout the process. Let $L$ be the specific enthalpy of fusion of ice (latent heat), and $v_i, v_w$ be the specific volumes of ice and water, respectively (assumed constant). Which of the following expressions gives the final pressure of the gas?

Options

A.
$P_0 \exp\left(\frac{mL}{nRT_0}\right)$
B.
$P_0 \exp\left(\frac{m[L - P_0(v_w - v_i)]}{nRT_0}\right)$
C.
$P_0 \left(1 + \frac{mL}{nRT_0}\right)$
D.
$P_0 \exp\left(\frac{mL}{nC_v T_0}\right)$

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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|Adiabatic Process Constraint|Integration

Why This Question Is Tricky

Common Mistakes

This question tests the coupling of a phase transition with the adiabatic constraint of a composite system.

Students often erroneously treat the phase change as an isolated isobaric process or attempt to manually subtract the $P \Delta V$ work of the ice-water transition from the latent heat.

The core trap lies in failing to recognize that in the differential First Law energy balance, the specific volume terms $P(v_w - v_i)$ perfectly absorb into the specific internal energy change to form the enthalpy of fusion $L$ .

Consequently, the gas pressure depends solely on the latent heat and the ideal gas law, completely independent of the specific volumes of the condensed phases.

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