JEE Main · 2020 · Shift-IIeasyTHERMO-046

Five moles of ideal gas at 1 bar and 298 K is expanded into vacuum to double the volume. The work done is:

Thermodynamics · Class 11 · JEE Main Previous Year Question

Question

Options

a
$C_v(T_2-T_1)$
b
$-RT(V_2-V_1)$
c
$-RT\ln V_2/V_1$
d
Zero
✓

Correct Answerd

Zero

Detailed Solution

🧠 Free expansion into vacuum: no opposing force, so no work is done $P_{\text{ext}} = 0$ (vacuum). Work = $-P_{\text{ext}} \cdot \Delta V = 0$ .

None of the other formulas apply:

(a) $C_v(T_2 - T_1)$ = $\Delta U$ , not work — and $\Delta T = 0$ for isothermal ideal gas anyway.
(b) and (c) are not standard work expressions for free expansion.

For free expansion of an ideal gas: $w = 0$ , $q = 0$ , $\Delta U = 0$ , $\Delta T = 0$ .

$\boxed{\text{Answer: (d)}}$

Practice this question with progress tracking

Want timed practice with adaptive difficulty? Solve this question (and hundreds more from Thermodynamics) inside The Crucible, our adaptive practice platform.

Practice in The Crucible →Browse Thermodynamics chapter →

More JEE Main Thermodynamics PYQs

2025medium

Two vessels A and B are connected via stopcock. Vessel A is filled with a gas at a certain pressure. The entire assembly is immersed in water and allowed to come to thermal equilibrium. After opening…

2024easy

Choose the correct option for free expansion of an ideal gas under adiabatic condition:

2019easy

An ideal gas is allowed to expand from 1 L to 10 L against a constant external pressure of 1 bar. The work done in kJ is:

2025hard

Arrange the following in order of magnitude of work done by the system / on the system at constant temperature: (a) |Wreversible| for expansion in infinite stage. (b) |Wirreversible| for expansion in…

2025hard

Which of the following graphs correctly represents the variation of thermodynamic properties of Haber's process? (N2(g) + 3H2(g) <= 2NH3(g))

View all 58 Thermodynamics PYQs →