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Question #42150

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The Question

A cylindrical vessel of cross-sectional area $A$ is placed in an elevator accelerating upwards with a constant acceleration $a$ . The vessel contains a mass $m$ of ice at $0^\circ\text{C}$ . A frictionless piston of mass $M$ rests on the ice, exposed to atmospheric pressure $P_0$ . Heat is slowly supplied until the ice completely melts into water at $0^\circ\text{C}$ . Let $L$ be the increase in internal energy per unit mass during melting. The densities of ice and water are $\rho_1$ and $\rho_2$ respectively ( $\rho_2 > \rho_1$ ). What is the total heat $Q$ supplied to the system? (where $g$ is the acceleration due to gravity)

Options

A.
$m L - m \left[ P_0 + \frac{(2M + m)(g+a)}{2A} \right] \left( \frac{\rho_2 - \rho_1}{\rho_1 \rho_2} \right)$
B.
$m L - m \left[ P_0 + \frac{M(g+a)}{A} \right] \left( \frac{\rho_2 - \rho_1}{\rho_1 \rho_2} \right)$
C.
$m L - m \left[ P_0 + \frac{(2M + m)g}{2A} \right] \left( \frac{\rho_2 - \rho_1}{\rho_1 \rho_2} \right)$
D.
$m L + m \left[ P_0 + \frac{(2M + m)(g+a)}{2A} \right] \left( \frac{\rho_2 - \rho_1}{\rho_1 \rho_2} \right)$

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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|Accelerated Frame Hydrostatics|Work-Energy Theorem Validity

Why This Question Is Tricky

Common Mistakes

This question tests the application of the First Law of Thermodynamics in a non-inertial frame involving a phase change with volume contraction.

The primary trap is ignoring the fluid's own center of mass shift (self-gravity work), leading students to only calculate the boundary work done on the piston.

It also tests the correct identification of effective gravity $g_{eff} = g+a$ and the strict sign convention for work when volume decreases.

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