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Question #42148

Difficulty: 8/10 | 🟢 Free

The Question

Two solid blocks, A and B, have constant heat capacities $C$ and $2C$ , and initial temperatures $3T_0$ and $2T_0$ respectively. They are placed inside a massive evacuated chamber whose walls are maintained at a constant temperature $T_0$ . The blocks are connected by a thermally conducting rod, allowing them to exchange heat with each other. Simultaneously, they lose heat to the chamber walls via non-linear Stefan-Boltzmann radiation. After a long time, the system reaches thermal equilibrium. What is the total change in entropy of the universe?

Options

A.
$C(4 - \ln 12)$
B.
$C \ln\left(\frac{343}{324}\right)$
C.
$C(4 - \ln 6)$
D.
$C(2 - \ln 12)$

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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

Calorimetry with Heat Loss|Entropy and Reversibility|Integration

Why This Question Is Tricky

Common Mistakes

This question tests the fundamental property of entropy as a state function and the rigorous definition of the 'universe' in thermodynamics.

The trap explicitly mentions 'non-linear Stefan-Boltzmann radiation' to intimidate students into attempting complex, unsolvable time-dependent path integrals, or alternatively, tricks them into assuming the blocks form an isolated system (ignoring the chamber) to use standard calorimetry formulas (leading to Option B).

By recognizing that the chamber acts as a massive thermal reservoir, students can bypass the path dependency entirely and simply evaluate the initial and final states of the blocks alongside the total heat transferred to the surroundings.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Thermal Properties of Matter - Class 11 Part 2
Concept	Calorimetry with Heat Loss
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free