The First Law of Thermodynamics

The First Law of Thermodynamics is a statement of conservation of energy applied to thermodynamic systems. It relates the change in internal energy of a system to the heat exchanged with its surroundings and the work done.

The Equation

$\Delta U = Q - W$

Where:

• $\Delta U$ is the change in internal energy of the system (J)
• $Q$ is the heat added to the system (J) — positive when heat flows in, negative when it flows out
• $W$ is the work done by the system (J) — positive when the system expands, negative when compressed

Sign Conventions

Work by Expansion

When a gas expands against a constant external pressure $P$, it does work on the surroundings:

$W = P \Delta V$

Where $\Delta V = V_{\text{final}} - V_{\text{initial}}$ is the change in volume. If the gas is compressed, $\Delta V < 0$ and the work is negative (work done on the system).

Examples

Isothermal process (constant temperature): If a gas absorbs 1000 J of heat and does 1000 J of work expanding, then $\Delta U = 1000 - 1000 = 0$. The internal energy does not change — consistent with constant temperature for an ideal gas.

Adiabatic compression: If no heat is exchanged ($Q = 0$) but 500 J of work is done on the gas ($W = -500$), then $\Delta U = 0 - (-500) = 500\,\text{J}$. The gas heats up.

Your Task

Implement the two functions below using the First Law equations.