Among the following the set of parameters that represents path functions, is
(A) q + W
(B) q
(C) W
(

Q: Why is $q+W$ a state function if both $q$ and $W$ are path functions?

According to the First Law of Thermodynamics, $q+W = \Delta U$. While individual values of heat and work depend on the path, their sum always equals the change in internal energy, which is strictly a state function.

Q: What exactly is $H - TS$?

This is the definition of Gibbs Free Energy ($G$). It combines enthalpy ($H$), temperature ($T$), and entropy ($S$) to predict the spontaneity of a process at constant temperature and pressure.

Q: Are there any other path functions besides heat and work?

In standard chemical thermodynamics, heat ($q$) and work ($W$) are the primary path functions you will encounter. Almost all other standard thermodynamic potentials ($U, H, S, G, A$) are state functions.

Q: Does the path matter for a cyclic process?

For a cyclic process, the initial and final states are the same. Therefore, the change in any state function (like $\Delta U$ or $\Delta H$) is zero. However, the net heat and work (path functions) are generally non-zero.

Q: How do I quickly identify a state function?

If a property can be assigned a definite value at a specific state (like a specific temperature, pressure, and volume), it's a state function. You can't say a system 'contains' a certain amount of work or heat; you can only measure them during a change.

Question

Among the following the set of parameters that represents path functions, is
(A) $q + W$
(B) $q$
(C) $W$
(D) $H - TS$

Options:

(A) (A) and (D)

(B) (A), (B) and (C)

(C) (B), (C) and (D)

(D) (B) and (C)

Sigma Percentile · Accepted Answer

### The Journey vs. The Destination

In the fascinating world of thermodynamics, every property of a system falls into one of two distinct categories: **state functions** and **path functions**.

Understanding the difference between them is like understanding the difference between climbing a mountain and simply knowing your altitude.

If you are standing at the summit, your altitude is a **state function**. It doesn't matter if you took the steep, treacherous path or the long, winding scenic route; your altitude is exactly the same.

However, the total distance you walked and the energy you expended are **path functions**. They depend entirely on the specific journey you chose.

### Analyzing Heat and Work

Let's apply this analogy to our thermodynamic parameters. Imagine a gas expanding in a cylinder, moving from an initial State 1 to a final State 2.

The heat exchanged with the surroundings, denoted as $q$, and the work done by the gas, denoted as $W$, are highly dependent on *how* the expansion happens.

Did it expand isothermally? Adiabatically? The values of $q$ and $W$ will change drastically based on the process. Therefore, **$q$ and $W$ are classic path functions**.

### The Magic of the First Law

Now, let's look at the expression $q + W$. Individually, they are path-dependent rebels. But what happens when we add them together?

According to the **First Law of Thermodynamics**, the sum of heat and work equals the change in the system's internal energy:

$$ \Delta U = q + W $$

Here is the beautiful part: Internal energy ($U$) is a fundamental property of the state of the system. It only cares about the current temperature, pressure, and volume, not the history of how the system got there.

Because $\Delta U$ is a state function, the sum **$q + W$ must also be a state function**, even though its individual components are not!

### Decoding Gibbs Free Energy

Finally, let's examine the expression $H - TS$. What does this represent?

This specific combination of variables defines the **Gibbs Free Energy** ($G$):

$$ G = H - TS $$

Let's break down its components. Enthalpy ($H$), Temperature ($T$), and Entropy ($S$) are all fundamental properties that describe the current state of a system. They do not depend on the path taken.

Since $H$, $T$, and $S$ are all state functions, any mathematical combination of them will also yield a state function. Therefore, **$H - TS$ is a state function**.

### The Final Verdict

We have systematically analyzed each parameter. We discovered that $q + W$ and $H - TS$ are state functions, locked to the initial and final states of the system.

The only parameters that depend on the specific thermodynamic journey are heat ($q$) and work ($W$).

Therefore, the correct set of path functions is (B) and (C), making option (d) the perfect answer.

Animated Solution for Chemistry - Chemical Thermodynamics: Among the following the set of parameters that represents path functions, is (A) $q + W$ (B) $q$ (C) $W$ (D) $H - T S$

Select Answer:

Visualized Solution

$S t a t e v s P a t h F u n c t i o n s$

$H e a t an d W or k$

$F i r s t L a w o f T h er m o d y nami cs$

$G ibb s F r ee E n er g y$

$C o n c l u s i o n$

The Sigma Insight: First Law of Thermodynamics

The Journey vs

Analyzing Heat and Work

The Magic of the First Law

Decoding Gibbs Free Energy

The Final Verdict

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Animated Solution for Chemistry - Chemical Thermodynamics: .math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Among the following the set of parameters that represents path functions, is (A) q+W (B) q (C) W (D) H−TS