Question

Which of the following are not path functions? 
I. H - T S 
II. W 
III. q 
IV. q + W 
 

• A. I and III
• B. I, II, IV
• C. II, III and IV
• D. I and IV

Hint:

State functions: depend only on initial and final states (e.g., H, U, S). Path functions: depend on how the change occurs (e.g., q, W).

Answer 1

The Correct Option is D

 

In thermodynamics, a path function is a quantity that depends on the specific process or path taken to get from one state to another. On the other hand, state functions are independent of the path and depend only on the initial and final states.

Let's analyze each of the options:

I. \( H - T S \)

This expression represents the Gibbs free energy (\( G = H - T S \)). Since the Gibbs free energy is a state function, it depends only on the initial and final states, not on the path taken. Therefore, \( H - T S \) is a state function and not a path function.

II. W (Work)

Work (\( W \)) is a path function because it depends on the specific process or path taken to change the system's state. It is not determined solely by the initial and final states of the system.

III. q (Heat)

Heat (\( q \)) is also a path function because it depends on the specific process through which energy is transferred to or from the system. The amount of heat exchanged can vary depending on the path taken, even if the initial and final states are the same.

IV. \( q + W \) (Total energy transfer)

The sum of heat (\( q \)) and work (\( W \)) is the total energy transfer in a process. Since both heat and work are path functions, their sum, \( q + W \), is also a path function. It depends on the process used, not just the initial and final states.

Final Answer:

The expressions that are not path functions are:

• I. \( H - T S \) (This is a state function, not a path function)