First Law of Thermodynamics — Definition

Definition

Imagine you have a sealed container of gas – that's your 'system'. Everything outside the container is the 'surroundings'. The First Law of Thermodynamics is like an energy accountant for this system. It tells us that energy can't just appear or disappear; it has to come from somewhere or go somewhere.

There are three main ways a system's energy can change:

1
Internal Energy ($Delta U$) — This is the total energy stored within the system, primarily due to the random motion and interactions of its molecules (kinetic and potential energy at the molecular level). When the temperature of the gas increases, its internal energy increases.
2
Heat ($Q$) — This is energy transferred between the system and its surroundings due to a temperature difference. If you heat the container, you're adding heat to the system. If the container cools down, it's losing heat.
3
Work ($W$) — This is energy transferred when a force acts over a distance. For a gas, this usually means the gas expanding and pushing a piston (doing work *on* the surroundings) or being compressed by a piston (work being done *on* the gas *by* the surroundings).

The First Law states that the change in the system's internal energy ($Delta U$) is equal to the heat added to the system ($Q$) minus the work done *by* the system ($W$). Mathematically, this is written as $Delta U = Q - W$.

Let's break down the signs:

If heat is *added* to the system, $Q$ is positive.
If heat is *removed* from the system, $Q$ is negative.
If the system *does work* on the surroundings (e.g., expands), $W$ is positive.
If work is *done on* the system by the surroundings (e.g., compressed), $W$ is negative.

So, if you add heat to a gas ($Q > 0$) and the gas expands, doing work ($W > 0$), its internal energy might increase, decrease, or stay the same depending on the relative magnitudes. If you add heat and the gas doesn't do any work (e.g., in a rigid container), all that heat goes into increasing its internal energy and thus its temperature. This law is fundamental because it applies to everything from engines to biological cells, explaining how energy is conserved and transformed.