First Law of Thermodynamics
The first law of thermodynamics is the principle of conservation of energy applied to thermodynamic systems: the change in internal energy ΔU of a closed system equals the heat Q added to the system minus the work W done by the system on its surroundings, ΔU = Q − W. Internal energy is a state function, while heat and work depend on the process.
Curious
The first law is energy conservation (see Conservation of Energy) extended to include heat. When you pump a bicycle tyre, the work you do warms the air; when steam pushes a piston, the gas loses internal energy as it does work. Every joule is accounted for.
This rules out a “perpetual motion machine of the first kind”, a device that produces work without any energy input. The law was established in the 1840s by Julius Robert Mayer, James Joule and Hermann von Helmholtz, after Joule showed that a fixed amount of mechanical work always produces the same amount of heating.
Exploring
| Process | Constraint | First law becomes |
|---|---|---|
| Isochoric (constant volume) | W = 0 | ΔU = Q |
| Isobaric (constant pressure) | W = pΔV | ΔU = Q − pΔV |
| Isothermal (ideal gas) | ΔU = 0 | Q = W |
| Adiabatic | Q = 0 | ΔU = −W |
| Cyclic | ΔU = 0 per cycle | Qnet = Wnet |
Deep Dive
Differential form. dU = δQ − δW, where δ marks inexact differentials: heat and work are not state functions, so their integrals depend on the path. For a simple compressible system doing reversible work, δW = p dV; combined with δQrev = T dS (see Entropy), this gives the fundamental relation dU = T dS − p dV, from which the thermodynamic potentials follow.
History. Mayer (1842) estimated the mechanical equivalent of heat from gas data; Joule (1843–1850) measured it directly with falling weights driving paddles in water, obtaining about 4.16 J per calorie in his 1850 paper, close to the modern 4.186 J. Helmholtz (1847) stated energy conservation as a general principle. Priority was disputed at the time, and historians generally credit all three with complementary roles.
Scope and limits. In open systems, enthalpy H = U + pV accounts for flow work. In relativity, internal energy includes rest-mass energy (see Mass-Energy Equivalence). Energy conservation follows from time-translation symmetry via Noether's theorem; in an expanding universe, a globally conserved total energy is not generally well defined, a subtle point in cosmology (see Dark Energy).
Concept Relationship Map
Requires: conservation of energy, zeroth law
Enables: second law, enthalpy, heat engines
Commonly confused with: the idea that bodies “contain heat”
Sources
- Joule, J.P. (1850). Philosophical Transactions of the Royal Society, 140, 61–82.
- Helmholtz, H. von (1847). Über die Erhaltung der Kraft. Berlin: G. Reimer.
- Callen, H.B. (1985). Thermodynamics and an Introduction to Thermostatistics (2nd ed.). Wiley.