1.3 The First Law of Thermodynamics

The First Law: Energy Conservation

The First Law of Thermodynamics states that a system's internal energy (ΔU) changes based on heat added and work done: ΔU = Q − W. Here, Q is heat added to the system (positive if absorbed) and W is work done BY the system (positive if the system expands). This is just conservation of energy applied to thermal systems.

Work Done by a Gas

For a gas, work (W) = PΔV when pressure is constant. If a gas expands (ΔV > 0), it does positive work on surroundings; if compressed (ΔV < 0), work done by gas is negative. On a PV diagram, work equals the area under the curve, and this depends on the path taken between states.

Special Thermodynamic Processes

Isothermal (constant T): ΔU = 0, so Q = W. Isobaric (constant P): W = PΔV. Isochoric/isovolumetric (constant V): W = 0, so ΔU = Q. Adiabatic (no heat exchange): Q = 0, so ΔU = −W. Recognizing these special cases simplifies applying the First Law.

Key terms

First Law of Thermodynamics

ΔU = Q − W; the change in internal energy equals heat added minus work done by the system.

Isothermal process

Constant temperature; ΔU = 0, so Q = W.

Adiabatic process

No heat exchange (Q = 0); ΔU = -W.

Isochoric process

Constant volume; W = 0, so ΔU = Q.

Work on a PV diagram

Equal to the area under the curve on a PV diagram; represents work done by or on the gas.

Try an AP-style question

100 J of heat is added to a gas while the gas does 40 J of work on its surroundings. What is ΔU? (ΔU = Q + W, W = work done on the gas)

1. +40 J
2. −60 J
3. +140 J
4. +60 J