16.2 The first law of thermodynamics

For constant external pressure, work done by a gas during a volume change is W=p∆V, with expansion positive for work done by the gas under the chosen convention.

State the sign convention and distinguish work by the gas from work on the gas. For changing pressure, use the area under a p–V graph.

A gas expanding by 0.020 m³ against 1.0×10⁵ Pa does 2000 J of work.

The formula is not automatically valid when pressure changes significantly, and sign depends on the convention used.

The first law is ∆U=q+W when q is energy supplied as heat and W is work done on the system; equivalent conventions may write ∆U=Q−W_by.

Declare the sign convention before substituting. Internal energy rises when net energy enters and falls when net energy leaves.

If 300 J of heat enters and the system does 100 J of work, ∆U=200 J using the q−W_by convention.

The first law is energy conservation, not a statement that heat and work are stored properties of the system.