PV-work sign depends on the convention
- 01
The tempting model
Mixing work done by the gas with work done on the gas in the same first-law equation.
- 02
Why it feels right
Both phrases use the word work, so the sign feels semantic rather than mathematical.
- 03
Where it breaks · how to catch it
Expansion sometimes increases and sometimes decreases internal energy in your equations without a sign convention change.
- 04
The correct model
State your convention. With ΔU = Q − W_by, expansion gives W_by > 0. With the work-on-gas convention, use ΔU = Q + W_on.
- 05
Repair · see it, then test it
worked example An insulated gas expands and does 20 J of work. What is ΔU using ΔU = Q − W_by?
Tempting move
+20 J.
Correct move
−20 J because Q = 0 and W_by = +20 J.
Test the repair TH-04 · transferinclude JMake a fresh prediction before referring to the worked example.