State functions are physical quantities that describe the current state of a system and are independent of the path taken to reach that state. This means that the value of a state function only depends on the current state of the system and not how it got there.
Some examples of state functions include temperature, pressure, volume, internal energy, and enthalpy. These quantities describe the state of a system and can be measured without knowing the history or path taken to reach that state.
Path functions, unlike state functions, depend on the path taken to reach a particular state. Examples of path functions include work and heat, which are both dependent on the process used to change the system's state.
State functions are important in thermodynamics because they allow us to describe and analyze thermodynamic systems without needing to know the specific process used to reach a particular state. This simplifies calculations and allows us to make predictions about a system's behavior.
According to the Second Law of Thermodynamics, a spontaneous process will always result in an increase in the entropy of the universe. Since entropy is a state function, we can use it to determine the spontaneity of a process by comparing the entropy of the initial state to the entropy of the final state. If the final state has a higher entropy, the process is spontaneous.