Thermodynamics applies energy conservation to systems that exchange energy with their surroundings. The first law shows how heating, cooling, and work change a system’s internal energy during a physical process.

The first law as energy accounting

When a thermodynamic system changes, physicists track energy crossing the system boundary. The central idea is ordinary conservation of energy: energy is not created or destroyed. Instead, it is transferred or transformed. In thermodynamics, the important question is how those transfers affect the system’s internal energy, written as $U$.

The first law is therefore a bookkeeping rule. It connects microscopic stored energy inside the system to energy entering or leaving during the process. If the system gains energy from its surroundings, $U$ must increase unless an equal amount leaves in another way. If the system loses more energy than it gains, $U$ decreases.

This AP Physics 2 sign convention treats work done on the system as positive.

That is why compression often gives $W>0$, while expansion often gives $W<0$. Keeping the sign convention consistent is more important than memorizing a single verbal rule.

Interpreting the three quantities

The term $\Delta U$ tells how the internal energy changes between an initial state and a final state. A positive value means the microscopic energy of the system increases. A negative value means the system ends with less internal energy than before.

The term $Q$ represents energy transferred because of a temperature difference. If energy enters the system by heating, then $Q>0$. If energy leaves the system by cooling, then $Q<0$. It is important to treat heating and cooling as energy transfer processes, not as material substances stored inside the system.

The term $W$ represents energy transferred by forces acting through a boundary displacement. In gas systems, this usually happens when a piston moves or when the gas changes volume.

A piston–cylinder sketch showing a gas expanding and pushing a piston, illustrating how boundary motion allows mechanical energy transfer as work. This makes the sign idea concrete: during expansion the gas does work on the surroundings (often corresponding to $W<0$ with your AP Physics 2 “work done on the system” convention). Source

If the surroundings squeeze the gas, they do work on it, so $W>0$. If the gas pushes outward on the surroundings, the gas does work on them, so $W<0$.

A pressure–volume (PV) diagram with a shaded region highlighting that work equals the area under the curve (or inside a closed loop for a cycle). This connects the graphical meaning of work to the energy-accounting equation $\Delta U = Q + W$ by making $W$ something students can compute from a process path. Source

What the first law says in physical situations

The first law combines the effects of thermal transfer and work. It does not care whether the process looks simple or complicated; the energy balance must still hold.

• If $Q>0$ and $W=0$, the system gains internal energy only by heating.

• If $Q<0$ and $W=0$, the system loses internal energy only by cooling.

• If $Q=0$ and $W>0$, work alone increases the internal energy.

• If $Q=0$ and $W<0$, the system loses internal energy because it does work on the surroundings.

• If both $Q$ and $W$ are nonzero, add them algebraically to find $\Delta U$.

This explains why a system can be heated and still have its internal energy decrease: if it does even more work on the surroundings, the negative work term can outweigh the positive heating term. It also explains why internal energy can stay constant when energy is transferred. If $Q$ and $W$ have equal magnitude and opposite overall effect, then $\Delta U=0$.

Why this is a statement of conservation of energy

The first law does not introduce a special kind of thermodynamic energy conservation. It is the same universal conservation law written for a chosen system. Any increase in the system’s internal energy must come from energy transferred in by heating or by work. Any decrease in internal energy means that energy has left the system through one or both of those mechanisms.

Because of this, the first law is especially useful for checking whether a description is physically possible. A claim that a gas expands, does work on the surroundings, and also increases its internal energy without any energy input would violate conservation of energy. The missing energy would have to come from somewhere, and the first law reveals that problem immediately.

Common sign and reasoning errors

Most mistakes on this topic come from poor sign choices rather than difficult physics. Always identify the system first, since the signs of $Q$ and $W$ depend on which object or collection of matter you are analyzing.

Helpful questions include:

• Is energy crossing the boundary because of a temperature difference?

• Is the surroundings doing work on the system, or is the system doing work on the surroundings?

• After combining $Q$ and $W$, should $\Delta U$ be positive, negative, or zero?

Using those questions keeps the first law tied to the core idea: every thermodynamic change must satisfy conservation of energy.