Sign Convention for Heat and Work in Thermodynamics (Positive and Negative)
Physics · Thermodynamics · NEET
In thermodynamics, heat Q is POSITIVE when it is added to the system (gas) and NEGATIVE when the gas gives out heat. Work W is POSITIVE when it is done BY the gas (gas expands) and NEGATIVE when work is done ON the gas (gas is compressed). Memory hook: "In is plus for heat, Out is plus for work" - heat coming IN is +, work going OUT is +.
Heat flowing INTO the gas is positive and heat leaving is negative; work done BY the gas (expansion) is positive and work done ON the gas (compression) is negative. Plug these signed values into Q = dU + W.
Your doubts, answered
Is heat added to the system positive or negative?
Heat added to the system (gas) is POSITIVE. When you heat a gas or the gas absorbs heat, write Q as a plus number. If the gas gives out heat (releases heat to surroundings), Q is NEGATIVE. Simple rule: heat coming IN is +, heat going OUT is -.
Is work done by the gas positive or negative?
Work done BY the gas is POSITIVE. When a gas expands, it pushes the piston out and does positive work. When the gas is compressed (work is done ON the gas), the work done by the gas is NEGATIVE. In short: expansion means +W, compression means -W.
Why is work done ON the gas taken as negative?
We always measure W as the work done BY the system in the standard NEET form Q = dU + W. If the surroundings push the piston in and compress the gas, the gas itself is doing negative work (it is receiving work, not giving it). So work done ON the gas enters the equation with a minus sign.
Should I use Q = dU + W or Q = dU - W?
Use Q = dU + W, where W is the work done BY the gas. This is the NCERT and NEET convention. You will see Q = dU - W in some chemistry books, but there W means work done ON the gas. Pick ONE convention and keep the signs consistent. For NEET Physics, always use Q = dU + W with W = work done by the gas.
What sign does internal energy change dU get?
dU is simply positive when the internal energy (and temperature) of the gas rises, and negative when it falls. dU is not a matter of convention - it depends only on temperature change for an ideal gas: dU = n Cv dT. If temperature goes up, dU is +; if temperature goes down, dU is -.
⚠️ The NEET trap ✗ A gas is compressed and 200 J of work is done, so students plug W = +200 J into Q = dU + W and get the internal energy change wrong by 400 J. ✓ Work done ON the gas is negative in the by-gas convention. Compression means the gas does W = -200 J, so dU = Q - W = Q + 200 J. Always convert 'work done ON the gas' to a negative W before using Q = dU + W. 🧠 Read the words 'work done BY' vs 'work done ON' very carefully.
Real NEET questions
NEET 2026
At a certain temperature, during a process, 500 J is absorbed by the system and 200 J of work is done by the system. The change in internal energy of the system is
A · A. 400 J
B · B. 300 J ✓
C · C. 700 J
D · D. 500 J
Solution: Use the first law Q = dU + W, so dU = Q - W. Apply the sign convention: heat absorbed by the system means Q = +500 J. Work done BY the system means W = +200 J. Then dU = 500 - 200 = 300 J. The internal energy rises by 300 J, so the answer is 300 J (option B). Notice both signs are positive here because heat came IN and work went OUT.
NEET 2026
An electric heater supplies heat to a system at a rate of 100 W. If the system performs work at a rate of 75 J/s, the rate at which internal energy increases is
A · A. 75 W
B · B. 100 W
C · C. 125 W
D · D. 25 W ✓
Solution: Write the first law in rate form: dQ/dt = dU/dt + dW/dt. Heat is supplied TO the system, so dQ/dt = +100 W (heat coming in is positive). The system performs work, so dW/dt = +75 J/s (work done by the system is positive). Then dU/dt = dQ/dt - dW/dt = 100 - 75 = 25 W. The internal energy increases at 25 W (option D).
Solved Thermodynamics NEET PYQs
Try the real previous-year questions from this chapter — each with the answer and a full solution.
What is the sign convention for heat and work in one line?
Heat added to the gas is positive, heat released is negative. Work done by the gas (expansion) is positive, work done on the gas (compression) is negative.
Which formula uses this sign convention in NEET?
The first law Q = dU + W, where Q is heat added to the gas and W is work done by the gas. Keep both signs consistent with this convention.
Is the physics sign convention the same as the chemistry one?
No. Physics (NCERT) uses Q = dU + W with W = work done by the gas. Chemistry often uses dU = Q + W with W = work done on the gas. The physics answer for NEET is Q = dU + W.
What is a quick memory trick for the signs?
IN is plus for heat, OUT is plus for work. Heat flowing IN to the gas is +Q; work going OUT (gas expanding) is +W.
Does dU have a convention too?
dU has no separate convention. It is positive if temperature (and internal energy) rises and negative if it falls, since dU = n Cv dT for an ideal gas.
