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Question #42348

Difficulty: 8/10 | 🟢 Free

The Question

A vertical, thermally insulated cylinder contains a rigid diatomic ideal gas. The cylinder is closed by a massless, thermally conducting piston of area $A$ that can move without friction. A block of mass $M$ rests on top of the piston. The external atmospheric pressure is $P_0$ . The block is given an initial horizontal velocity $v_0$ . Due to kinetic friction between the block and the piston, the block eventually comes to rest relative to the piston. The piston is constrained to move only vertically. Assuming all the heat generated by friction is absorbed by the gas, what is the ratio of the work done by the gas to the initial kinetic energy of the block?

Options

A.
$\frac{2}{7}$
B.
$\frac{5}{7}$
C.
$\frac{2}{5}$
D.
$1$

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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

Work Done by Friction|Entropy and Reversibility|Approximations

Why This Question Is Tricky

Common Mistakes

This question tests the student's ability to link dissipative mechanical work to the First Law of Thermodynamics in an isobaric process.

A common trap is assuming that all dissipated mechanical energy directly equals the work done by the gas ( $W = Q$ ), ignoring the change in internal energy.

Another frequent mistake is using the isochoric molar heat capacity ( $C_v$ ) instead of the isobaric one ( $C_p$ ), or calculating the fraction of energy converted into internal energy ( $\frac{5}{7}$ ) rather than the work done.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Work, Energy, and Power - Class 11 Part 1
Concept	Work Done by Friction
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free