NCERT says 'No work is done during free expansion of an ideal gas whether the process is reversible or irreversible' — Here's how NEET tests it

NCERT Line-by-Line

1. TITLE

NCERT says 'No work is done during free expansion of an ideal gas whether the process is reversible or irreversible' — Here's how NEET tests it

2. THE NCERT STATEMENT

NCERT EXACT LINE:
"No work is done during free expansion of an ideal gas whether the process is reversible or irreversible".
— NCERT Class 11, Chapter 5 (Chemical Thermodynamics), Page 142.

3. WHY THIS LINE MATTERS

• How many times has NEET tested this? Highly tested, both directly in standalone MCQs and indirectly in numerical problems where students waste time trying to calculate work using volume changes.
• What makes this statement tricky? Students are taught that reversible processes yield maximum work. When they see the word "reversible" paired with "expansion," they instinctively look for a non-zero work value using formulas like $W_{rev}=-2.303~nRT~log(V_{f}/V_{i})$.
• What do students typically misremember? They forget that "free expansion" means expansion into a vacuum, where the external pressure ($p_{ex}$) is strictly zero. Without external pressure to push against, work simply cannot be done, regardless of how slow or fast the process is.

4. MCQ

According to NCERT, during the free expansion of an ideal gas into a vacuum:
A) No work is done whether the process is reversible or irreversible.
B) No work is done only if the process is irreversible.
C) Maximum work is obtained because the volume increases.
D) Maximum work is done by the system on the surroundings.

5. ANSWER + LINE BREAKDOWN

Correct Answer: A

Break down the NCERT line:
- "No work is done" means $w = 0$. In thermodynamics, mechanical work requires an external opposing force, calculated as $w = -p_{ex}\Delta V$.
- "Free expansion of an ideal gas" means the gas is expanding into a vacuum where the opposing external pressure ($p_{ex}$) is exactly zero.
- "whether the process is reversible or irreversible" means the path or speed of the expansion doesn't matter. Since you are multiplying by $p_{ex} = 0$, the mathematical result is always zero.
- The key word is "free" because it is the code word for a vacuum ($p_{ex} = 0$), immediately nullifying any PV-work calculations.

6. HOW NEET TWISTS THIS

Show 3 ways NEET can ask the same fact:
- As an assertion-reason:
Assertion: No work is done during the free expansion of an ideal gas whether reversible or irreversible.
Reason: In a vacuum, the external pressure ($p_{ex}$) is zero. (Answer: Both A and R are true, and R is the correct explanation of A).
- As a direct question: "For an ideal gas undergoing free expansion into a vacuum, what is the value of work done ($w$)?" (Answer: $w = 0$).
- As an except question: "All of the following are true for the free isothermal expansion of an ideal gas EXCEPT..." (Answer: Work done is equal to $-2.303 nRT \log(V_2/V_1)$).

7. MEMORY LOCK

MEMORIZE:
Free Expansion = Zero Pressure = Zero Work. (Reversible or not, vacuum means nothing to push against!)
Mnemonic: FREE means Free of Resistance, exactly Empty, Energy unchanged ( $\Delta U = 0$, $w=0$, $q=0$ ).

8. RELATED NCERT LINES

Also remember these from the same page:
- "For isothermal ($T = constant$) expansion of an ideal gas into vacuum; $w=0$ since $p_{ex}=0$."
- "Also, Joule determined experimentally that $q=0$; therefore, $\Delta U=0$."

9. NCERT REFERENCE

NCERT Class 11, Chapter 5 (Chemical Thermodynamics), Page 142, Paragraph 4.

10. CTA

All important NCERT lines from this chapter → Chemical Thermodynamics Guide