TheoremProved

The first law of thermodynamics

Statement

$\Delta U = Q - A$ — the change in a system’s internal energy equals the heat it absorbs minus the work it performs.

Why is it true?

This is simply energy conservation applied to thermal processes: energy is neither created nor destroyed, only converted between heat, work, and internal energy.

A virtual piston in a cylinder: add heat Q or compress/expand the gas to do work, then watch the internal energy U change exactly per ΔU = Q + W.

Stated by

stated 1850Rudolf Clausius stated 1850James Prescott Joule

Topics that use this theorem

The first law of thermodynamics

Step-by-step proofs

No step-by-step proof yet for this theorem.

References

Rudolf Clausius (1850). The Mechanical Theory of Heat