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: Understanding the Concept:
Properties of a system are of two kinds. Extensive properties depend on the amount of matter present, and intensive properties do not. Separately, state functions depend only on the initial and final states, while path functions depend on how the change is carried out.

Step 2: Key Approach:
We need a property that is extensive and also a path function. So we first pick out the path function, then check that it scales with the amount of matter.

Step 3: Check Heat:
Heat \(q\) is energy that crosses the boundary because of a temperature difference. Its value is different for a reversible and an irreversible route between the same two states, so it is a path function. Doubling the amount of substance doubles the heat needed for the same temperature change, so it is extensive. So (A) satisfies both conditions.

Step 4: Why the other options are wrong:
Free energy \(G\), enthalpy \(H\) and entropy \(S\) are all extensive, but each is a state function. Their change between two states is fixed, whatever the path. So they fail the "depends on path" condition, and (B), (C) and (D) are wrong.

Final Answer:
Heat is both extensive and a path function. \[ \boxed{\text{Heat (option A)}} \]