First Law and Thermodynamic Sign Convention
Using the convention Q positive into the system and W positive when done by the system, the first law is ΔU = Q − W; reversing the work convention requires changing the written sign consistently rather than mixing conventions.
Why this shows up in the exam
Heat-work accounting in a piston · Power and energy-rate balances · Finding an unknown heat or work along a path
Learn the idea
Energy conservation links heat supplied, work done by the system, and change in internal energy. Track energy crossing the boundary: supplied heat raises stored energy unless part of it leaves as mechanical work.
🧠 Memory hook: Heat in minus work out equals stored-energy rise.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- ΔU = Q - W_by — finite-process first law with heat into the system and work by the system positive
- dU = δQ + δW_on — equivalent differential form when work done on the system is defined positive
How to approach it
- 1Write the sign convention before substituting
- 2Mark each energy transfer as into or out of the system
- 3Check that the final balance conserves energy
Common slip-ups that cost marks
- •Using ΔU = Q + W while calling W work by the gas
- •Treating heat and work as properties contained in a state
- •Ignoring the sign of rejected heat or compression work
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
A gas absorbs 500 J of heat and does 200 J of work. What is the change in its internal energy?
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