Before You Begin

Question #42575

Difficulty: 8/10 | 🟢 Free

The Question

One mole of a real gas obeys the modified equation of state $\left(P + \frac{a}{V^2}\right)V = RT$ , where $a$ is a positive constant, $P$ is pressure, $V$ is molar volume, $T$ is absolute temperature, and $R$ is the universal gas constant. The gas undergoes a reversible isothermal expansion from an initial volume $V_0$ to a final volume $2V_0$ at a constant temperature $T_0$ . Which of the following correctly represents the heat absorbed $Q$ and the work done $W$ by the gas during this process?

Options

A.
$Q = RT_0 \ln 2$ , $W = RT_0 \ln 2 - \frac{a}{2V_0}$
B.
$Q = RT_0 \ln 2 + \frac{a}{2V_0}$ , $W = RT_0 \ln 2$
C.
$Q = RT_0 \ln 2 - \frac{a}{2V_0}$ , $W = RT_0 \ln 2 - \frac{a}{2V_0}$
D.
$Q = RT_0 \ln 2 + \frac{a}{2V_0}$ , $W = RT_0 \ln 2 - \frac{a}{2V_0}$

Check Your Answer

Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Variable_Constraint

Develop pure symbolic logic skills by mastering algebraic constraints without relying on numerical data.

Concepts Behind This Question

Ideal Gas Assumptions|Carnot Engine Efficiency|Entropy and Reversibility

Why This Question Is Tricky

Common Mistakes

This question tests the candidate's understanding of the First Law of Thermodynamics and entropy for non-ideal gases.

A common trap is instinctively assuming that internal energy depends only on temperature, which implies $\Delta U = 0$ for any isothermal process.

If candidates make this ideal-gas assumption for a real gas, they will incorrectly conclude that $Q = W$ and choose option C.

By requiring the application of Maxwell's relations to find the exact entropy change, or by forcing the derivation of the volume-dependent internal energy term $\Delta U = a/(2V_0)$ , the problem distinguishes between rote memorization of ideal gas formulas and true thermodynamic maturity.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Kinetic Theory - Class 11 Part 2
Concept	Ideal Gas Assumptions
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free