First-Law Accounting: Heat, Work, and Internal Energy

Track energy entering and leaving a thermodynamic system. Positive and negative signs have physical meaning, not just algebraic meaning.

Heat, Q+600 J
Work by system, W+250 J
Change, ΔU+350 J
Initial internal energy2000 J
Final internal energy2350 J

Energy transfers

+600 J
Q > 0: heat enters. Q < 0: heat leaves.
+250 J
W > 0: system does work. W < 0: work is done on system.
2000 J
Used to visualize the final energy level Uf.
ΔU = Q − W,    Uf = Ui + Q − W
Heat sign: \(Q>0\) means energy crosses the boundary into the system as heat; \(Q<0\) means heat leaves.
Work sign: \(W>0\) means the system does work on the surroundings; \(W<0\) means the surroundings do work on the system.
Internal energy increases: The system receives 600 J as heat and sends 250 J out as work, leaving a net gain of 350 J.

System boundary and energy flow

surroundings SYSTEM closed thermodynamic system U = 2350 J ΔU = +350 J Q = +600 J W = +250 J heat enters work leaves
heat transfer Q work W internal energy U

Internal-energy level

Uᵢ U𝒇 2000 J 2350 J +350 J
Accounting, not “stored heat”: A system stores internal energy. Heat and work describe energy crossing the system boundary during a process.
Predict before moving a slider

Set Q = +500 J and W = +500 J. What happens to internal energy?