Question

Which of the following properties of a system depends upon the amount of matter and path?

• A. Heat
• B. Free energy
• C. Enthalpy
• D. Entropy

Hint:

Heat is a path function and also extensive, while H, G and S are state functions.

Answer 1

The Correct Option is A

Step 1: What the question asks:
Two things must hold together: the quantity grows with the size of the system, and it changes with the route taken.

Step 2: Sort the four options:
Write each as state function or path function. $G$, $H$ and $S$ are state functions. Heat $q$ is the only path function in the list.

Step 3: Confirm the size dependence:
For a given temperature rise, $q = mc\Delta T$. The mass $m$ appears directly, so $q$ doubles when the amount doubles. It is therefore extensive.

Step 4: Rule out the rest:
Enthalpy, free energy and entropy are extensive but their changes are fixed by the end states alone. Route does not matter for them, so none of them can be the answer.

Final Answer:
The only property in the list that is both extensive and route dependent is heat. \[ \boxed{A:\ \text{Heat}} \]