Question

Why is enthalpy a state function?

Answer 1

Hint: Enthalpy is a thermodynamic quantity that measures the heat changes that take place in the system or the surroundings at constant pressure. The first law of thermodynamics deals with the calculations of enthalpy under various conditions.

Complete answer:
Thermodynamics contains two types of functions that are called path functions and state functions or state variables.
Path functions are those thermodynamic quantities that are not measured in an independent manner and their measurements are sensitive to the path chosen to bring a particular change. Examples of path functions include work and heat that give different values when calculated for a reversible process and an irreversible process.
State functions are the variables in thermodynamics that are only dependent on the initial and final state of the thermodynamic process and remain unaltered by the path through which the process is accomplished. Change in state functions is therefore expressed as the difference between the final and the initial value, the path taken or the intermediate states are completely ignored in calculations.
Enthalpy is the heat change calculated at constant pressure and its values simply depend upon the initial and final states. Moreover, enthalpy as a function can be expressed as a linear combination of three other state variables namely internal energy, pressure and volume. The expression for enthalpy can be written as follows:
$$H=U+PV$$
$$\Rightarrow$$ Therefore enthalpy is a state function.

Note:
 Since enthalpy is a state function and change in enthalpy can be expressed as the difference of the final and initial state, the cyclic integral of enthalpy will always be zero. As a cyclic process involves the same initial and final state and therefore there is no change.