Mistakes/Tricks
1. TITLE
Sign Convention for Work and Heat: The silly mistake that costs 4 marks
2. THE MISTAKE STATEMENT
THE COMMON MISTAKE:
Most students calculate the internal energy change ($\Delta U$) incorrectly because they confuse the sign conventions for work ($w$) and heat ($q$). Specifically, students constantly get confused about when to use $+w$ (work done on the system) versus $-w$ (work done by the system).
3. WHY THIS MISTAKE HAPPENS
- What's the source of confusion? The ultimate trap is that Physics and Chemistry use completely different sign conventions! In Physics, work done by the system is often taken as positive because the focus is on the work a machine produces. However, Chemistry strictly follows the IUPAC convention, which focuses on the internal energy of the system.
- How do coaching centers sometimes teach this wrong? Teachers often teach Thermodynamics in Physics and Chemistry simultaneously but fail to emphasize that Physics books still follow the old convention where expansion work is positive. If you apply Physics rules to a Chemistry MCQ, you will instantly lose 4 marks.
4. THE CORRECT UNDERSTANDING
THE TRUTH:
In Chemical Thermodynamics, we are solely focused on the system's "energy budget." Any energy entering the system is positive, and any energy leaving the system is negative.
Work done ON the system ($+w$) is: Energy transferred into the system through mechanical or electrical means (like compression or stirring), which increases the system's internal energy.
Work done BY the system ($-w$) is: Energy the system expends to do mechanical work (like gas expansion), which decreases its internal energy.
Key difference: If the system is gaining energy (compression, being heated), the sign is positive (+). If the system is losing energy (expansion, cooling down), the sign is negative (-).
5. COMPARISON TABLE
| Aspect | Work done ON system ($+w$) | Work done BY system ($-w$) |
|---|---|---|
| Definition | Work is performed by the surroundings onto the system. | Work is performed by the system against the surroundings. |
| Energy Change | Internal energy ($U$) increases. | Internal energy ($U$) decreases. |
| Volume Change | Volume decreases ($\Delta V < 0$) — Compression. | Volume increases ($\Delta V > 0$) — Expansion. |
| Formula | $w = -p_{ex}(-\Delta V) = +ve$ | $w = -p_{ex}(+\Delta V) = -ve$ |
| NEET asks about | "Compression", "mixing", or "stirring". | "Expansion" or "gas pushes a piston". |
6. MCQ (Tests the exact confusion point)
A closed system absorbs $200 \text{ J}$ of heat from its surroundings. During this process, the system expands and does $150 \text{ J}$ of work on the surroundings. What is the change in internal energy ($\Delta U$)?
(a) $+350 \text{ J}$
(b) $+50 \text{ J}$
(c) $-350 \text{ J}$
(d) $-50 \text{ J}$
7. ANSWER + WHY THE TRAP WORKS
Correct: (b) $+50 \text{ J}$
"If you chose (a) $+350 \text{ J}$, you made the classic mistake of applying the Physics sign convention!"
The question specifically stated the system absorbs heat ($q = +200 \text{ J}$) and the system does work on the surroundings (expansion), which means energy is leaving the system ($w = -150 \text{ J}$).
Applying the First Law of Thermodynamics: $\Delta U = q + w$.
$\Delta U = (+200 \text{ J}) + (-150 \text{ J}) = +50 \text{ J}$.
If you simply added them together, you fell right into the examiner's trap!
8. THE TRICK TO NEVER FORGET
MEMORY TRICK:
Think of the System as your Bank Account.
- Money IN (Deposit) = Positive (+): Heat absorbed by the system ($+q$) or Work done ON the system ($+w$) increases your energy balance.
- Money OUT (Withdrawal) = Negative (-): Heat released by the system ($-q$) or Work done BY the system ($-w$) decreases your energy balance.
Relatable Indian Example: Imagine riding your bicycle up a steep Ghat (hill). The work done on the system (you, the cyclist) by your legs is positive, and your internal energy (stored potential energy) increases.
9. RAPID FIRE — Test Yourself
Quick check — Which one?
- An ideal gas expands against a constant external pressure. → $+w$ or $-w$?
- $50 \text{ J}$ of heat is released by the system. → $+q$ or $-q$?
- A student forcefully pushes a piston down into a cylinder of gas. → $+w$ or $-w$?
Answers:
1- [$-w$, because the gas expands, meaning the system does the work],
2- [$-q$, because heat is transferred from the system],
3- [$+w$, because work is done on the system via compression].
10. NCERT REFERENCE
IUPAC convention for Work ($w$) is defined in: NCERT Chemistry Class 11, Part 1, Chapter 5, Page 139.
IUPAC convention for Heat ($q$) is defined in: NCERT Chemistry Class 11, Part 1, Chapter 5, Page 139.
11. CTA
More comparisons from this chapter → Chemical Thermodynamics Guide