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Question #42542

Difficulty: 8/10 | 🟢 Free

The Question

One mole of an ideal diatomic gas is confined in a horizontal cylinder by a movable piston of cross-sectional area $A$ . The external pressure is constant at $P_0$ . Initially, the gas is in thermal and mechanical equilibrium with volume $V_0$ . A heater slowly supplies heat to the gas, causing it to expand. During the expansion, the piston experiences a non-conservative resistive force $f = kx$ (where $x$ is the displacement of the piston from its initial position) in addition to the external pressure. The work done against this resistive force is entirely dissipated as heat into the gas. The heating is stopped when the volume of the gas reaches $2V_0$ and its pressure reaches $2P_0$ . What is the total heat $Q$ supplied by the heater during this process?

Options

A.
$\frac{17}{2} P_0 V_0$
B.
9 P_0 V_0
C.
8 P_0 V_0
D.
12 P_0 V_0

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

Molar Heat Capacity (Cv vs Cp)|Conservative vs Non-conservative|Work-Energy Theorem

Why This Question Is Tricky

Common Mistakes

This question tests the application of the First Law of Thermodynamics in the presence of internal non-conservative forces.

A common fatal error (trap) is equating the work done by the gas ( $W_{gas} = \int P dV$ ) directly to the net energy leaving the system as work, leading to $Q_{heater} = \Delta U + W_{gas} = 9 P_0 V_0$ .

However, when the piston does work against friction and that energy is dissipated as heat back into the gas, the net energy leaving the system as work is only the work done against the external pressure ( $W_{ext}$ ).

Students must recognize that $Q_{net} = Q_{heater} + W_{friction}$ , requiring them to subtract the frictional work from the total thermodynamic heat to find the actual heat supplied by the external heater.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Thermodynamics - Class 11 Part 2
Concept	Molar Heat Capacity (Cv vs Cp)
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free