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The First Law of Thermodynamics is energy conservation applied to thermodynamic systems: ΔU = Q − W, where ΔU is the change in internal energy, Q is heat added to the system, and W is work done by the system. Internal energy is a state function — it depends only on the current state (T, P, V) of the system, not on the path taken. Heat and work are not state functions; they describe energy transfers during a process, not stored quantities.
Apply the first law to several simple cases: a gas heated at constant volume (W = 0, so Q = ΔU), a gas expanded without heat exchange (Q = 0, adiabatic), and isothermal expansion of an ideal gas (ΔU = 0, so Q = W). These limiting cases build physical intuition.
The First Law of Thermodynamics is energy conservation reformulated for systems that can exchange energy in two distinct ways: heat and work. You already know energy conservation from mechanics (kinetic plus potential energy is constant in a closed system). The First Law extends that idea to include thermal energy and opens up two new channels for energy transfer.
The statement is ΔU = Q − W, where ΔU is the change in the system's internal energy, Q is heat added to the system, and W is work done by the system. The sign conventions matter enormously. Q is positive when energy flows in as heat; W is positive when the system expands and pushes on its surroundings. A compressed gas that expands (W > 0) is doing work on something external; a pump compressing a gas (W < 0) is having work done on it. Getting these signs wrong is the primary source of error in applying the First Law.
The most important conceptual distinction is between internal energy (a state function) and heat and work (process quantities). Internal energy is a property of the system right now — it depends only on temperature, pressure, and volume, not on the history of how the system got there. Heat and work, by contrast, are not properties of a state; they describe energy transfers that happen during a process. You cannot open a gas cylinder and measure how much "heat" is in the gas — you can measure its internal energy (via temperature), but the heat it absorbed over its history is no longer physically meaningful. Saying a system "contains heat" is like asking how much "walking" is in your legs.
The First Law becomes most useful when applied to limiting cases that build intuition. At constant volume (no expansion possible), W = 0 and ΔU = Q: all the heat goes directly into raising internal energy, which is why heating a gas in a rigid tank raises its temperature predictably. In an adiabatic process (insulated walls, Q = 0), ΔU = −W: any work done on the gas raises its temperature, and any work done by the gas cools it. This is why rapidly expanding gases cool (aerosol cans, refrigeration) and rapidly compressed gases heat up (diesel ignition). For isothermal expansion of an ideal gas, ΔU = 0 forces Q = W — heat flows in to exactly compensate for the work done, keeping temperature constant.
The First Law tells you what energy balance must hold, but it does not tell you which processes are physically possible. Any process satisfying ΔU = Q − W is energetically legal — including a refrigerator running backwards and spontaneously concentrating heat into a hot reservoir. The Second Law is what rules those processes out. The First Law is necessary but not sufficient for predicting which direction thermodynamic processes actually go.