First Law (ΔU)⚠ unverified
Physics / Thermodynamics · Internal-energy change from the first law of thermodynamics
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| Q | Q | J | 500.0 | Heat added to system |
| W | W | J | 200.0 | Work done by system |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| delta_u | ΔU | J | Internal energy change |
The science & history
Understanding the Parameters
- $Q$ — positive when the system gains heat; negative when it rejects heat.
- $W$ — positive when the system does work on the surroundings (expansion work, shaft work out).
- $\Delta U$ — state function for a simple compressible system; path-independent between states, while $Q$ and $W$ are path-dependent.
Derivation (Approaching a Proof)
Energy conservation for a closed system (no mass flow): energy increase equals heat in minus work out,
$$\Delta E_{\mathrm{sys}} = Q - W.$$
If macroscopic KE/PE of the system as a whole are unchanged, $\Delta E = \Delta U$, hence $\Delta U = Q - W$. This is a statement of the first law, not a consequence of mechanics alone.
History
Joule’s mechanical equivalent of heat and mid-19th century thermodynamics established energy conservation including heat; the $Q-W$ bookkeeping is standard in engineering thermo textbooks (Çengel, Moran, etc.).
Related Concepts: Thermal Efficiency, Second Law Entropy, Enthalpy Moist Air, Entropy Change Ideal Gas
Notes: Registry calculator first-law-delta-u (unverified). Closed-system, engineering sign
convention. Filename uses ASCII DeltaU per SCHEMA (Δ avoided).