Question

Which of the following is a path function?
(a) Internal energy
(b) enthalpy
(c) work
(d) entropy

Answer 1

Hint: Path functions are those functions whose values or the properties depend on the initial and final states of the system. The thermodynamic property which has the formulas as; $P\mathrm{\Delta }V$ depends on the initial and the final states of the system. Now you can easily identify that property from the given thermodynamic quantities.

Complete answer:
First of all, let's discuss what a path function is. Path function is a thermodynamic property whose value depends on both the states of the system i.e. the initial stage of the system as well as the final stage of the system.
In simple terms, we can say that path function depends upon the path of the system.
Now considering the statement;
From all the above given thermodynamic quantities, work is the only property which depends on the path followed by the system i.e. on the initial and the final states of the system.
On the contrary, the rest all others i.e. internal energy, enthalpy and entropy are path independent.

Hence, option (c) is correct.

Note:
Don’t get confused in the state function and the path function. The state function doesn’t depend upon the path of the system i.e. it is independent of the initial and the final states of the system. Example:- internal energy , entropy etc.
whereas on the other hand, the path function depends upon the path of the system i.e. it is dependent on the initial and the final states of the system. Example: heat, work etc.