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Question #42164

Difficulty: 8/10 | 🟢 Free

The Question

An ideal diatomic gas is confined in a perfectly insulated cylinder with a movable piston. The gas is in thermal equilibrium and its radiation spectrum approximates that of a perfect blackbody. Initially, the internal energy of the gas is $U_0$ and its spectral emissive power peaks at a wavelength $\lambda_0$ . The gas undergoes an adiabatic expansion until the peak wavelength of its emitted radiation shifts to $2\lambda_0$ . Which of the following represents the work done by the gas and the ratio of its final volume to initial volume $\left(\frac{V_f}{V_0}\right)$ , respectively?

Options

A.
$\frac{U_0}{2}, 4\sqrt{2}$
B.
$U_0, 4\sqrt{2}$
C.
$\frac{U_0}{2}, 2\sqrt{2}$
D.
$-\frac{U_0}{2}, \frac{1}{4\sqrt{2}}$

Check Your Answer

Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Intuition_Breaker

Train your brain to resist "obvious" answers that are designed to deceive your intuition.

Concepts Behind This Question

Wien’s Displacement Law|Internal Energy Dependency|Adiabatic/Isothermal Processes

Why This Question Is Tricky

Common Mistakes

This question tests the synthesis of Modern Physics (Wien's Displacement Law) and Thermodynamics (Adiabatic processes and Internal Energy).

The primary trap lies in students failing to recognize that the peak emission wavelength acts as a direct proxy for the gas's absolute temperature.

A common mistake is assuming $T \propto \lambda$ instead of $T \propto 1/\lambda$ , leading to incorrect internal energy calculations.

Additionally, students often use the wrong degrees of freedom (e.g., monoatomic instead of diatomic) when calculating the adiabatic volume expansion ratio, which tests their attention to the specific thermodynamic constraints of the gas.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Thermal Properties of Matter - Class 11 Part 2
Concept	Wien’s Displacement Law
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free