First Law of Thermodynamics

The first law of thermodynamics is a generalized form of energy conservation stating that the change in internal energy equals the heat added to the system minus the work done by the system. Mathematically, ΔU = Q - W. This principle applies to all thermodynamic processes and relates three fundamental quantities: internal energy change, heat transfer, and work performed.

Internal energy is a state function because its change depends only on the system's initial and final equilibrium states, not on the path taken between them. Although heat and work individually depend on the thermodynamic path, their difference—the change in internal energy—is path independent. This makes internal energy similar to potential energy in mechanics.

Heat added to a system increases its internal energy, while heat removed decreases it. When a gas expands and does work on its surroundings, its internal energy decreases. Conversely, when work is done on the system, internal energy increases. The net effect on internal energy depends on the balance between heat transfer and work done.

Heat is positive when added to the system and negative when removed from it. Work is positive when done by the system and negative when done on the system. This convention ensures consistent application of the first law equation ΔU = Q - W across all thermodynamic processes and calculations.

In a sky lantern, the candle's heat increases the internal energy of air molecules inside, causing air expansion and inflation. As air expands, it does work on the lantern walls. The reduced air density creates lift. This example illustrates how heat transfer increases internal energy, which then performs work, demonstrating energy conservation in action.

Internal energy is a function of thermodynamic variables including pressure, temperature, and volume. These state variables completely describe a system's condition. Since internal energy depends only on these variables and not on how the system reached its current state, it qualifies as a state function, similar to other path-independent quantities.

In cyclic processes, a system returns to its initial state, so the total change in internal energy is zero. According to the first law, the net heat transfer into the system must equal the net work done by the system. This relationship holds for cyclic processes and helps analyze engines and refrigeration cycles.