state function

Meaning: A state function is a property fixed by the current condition of the system (such as its P, V, T and amount of gas), not by how it got there. Its change between two states is the same along any path. Pressure, volume, temperature, internal energy U, enthalpy H, entropy S and Gibbs free energy G are state functions; work and heat depend on the path. Over a full cycle that returns to the start, the change in a state function is zero.

Equation: ΔU = Q − W, where ΔU is the change in internal energy (J), Q is heat added to the system (J), and W is work done by the system (J). Only ΔU is path independent.

On the MCAT: A gas goes from state A to state B on a PV diagram by two different routes. ΔU and ΔT are the same on both; W (the area under the curve) and Q differ. In a closed cycle ΔU = 0, so net Q equals net W, and the enclosed area is the net work.

Common confusion: Because Q − W gives a state function, students assume Q and W are state functions too. Each one alone depends on the path. For an ideal gas, U depends on temperature alone, so any isothermal change has ΔU = 0 by any path.