Internal energy
The total kinetic and potential energy of all particles in a substance, related to temperature and state (solid, liquid, gas). Changes in internal energy arise from heat transfer (Q) and work done (W): ΔU = Q − W (first law of thermodynamics). Internal energy depends only on temperature for ideal gases but also on pressure and volume for real substances.
Formula
ΔU = Q − W
Real World
When NASA's Mars rovers compress gas in their actuators, the gas heats up as work is done on it — demonstrating that internal energy increases even without direct heat transfer.
Exam Focus
Sign convention matters: W is work done BY the system — if work is done ON the system, substitute a negative W or restate the equation clearly.
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