The internal energy change when a system goes from state A to B is 40 kJ/mol. If the system goes fro

Q: Does the reversibility of the path affect the internal energy change?

No, internal energy is a state function. Its change depends only on the initial and final states, completely independent of the path taken, whether reversible or irreversible.

Q: What about work and heat? Would their net change be zero too?

No. Work ($W$) and heat ($q$) are path functions. Their values depend heavily on the specific path taken. In a cyclic process, the net work done or net heat exchanged is generally not zero.

Q: Why is the 40 kJ/mol information given if the answer is zero?

It's a distractor! It tests your conceptual clarity. If the forward path has a change of $+40\text{ kJ/mol}$, the return path between the exact same states will inherently have a change of $-40\text{ kJ/mol}$, making the sum zero.

Q: What exactly is a cyclic process?

A cyclic process is a series of thermodynamic changes where the system eventually returns to its exact original state. The initial and final states are identical.

Q: Are there other properties that would be zero in this cyclic process?

Yes! Any state function will have a net change of zero in a cyclic process. This includes Enthalpy ($\Delta H = 0$), Entropy ($\Delta S = 0$), Gibbs Free Energy ($\Delta G = 0$), Pressure ($\Delta P = 0$), and Volume ($\Delta V = 0$).

Question

The internal energy change when a system goes from state $A$ to $B$ is $40	ext{ kJ/mol}$. If the system goes from $A$ to $B$ by a reversible path and returns to state $A$ by an irreversible path, what would be the net change in internal energy?

Options:

(A) $40	ext{ kJ}$

(B) $>40	ext{ kJ}$

(C) $< 40	ext{ kJ}$

(D) zero

Sigma Percentile · Accepted Answer

### The Magic of State Functions in Thermodynamics

When studying thermodynamics, one of the most profound realizations is understanding the difference between a **state function** and a **path function**. This simple conceptual distinction is the key to unlocking many complex problems, just like the one we are tackling here.

Imagine you are climbing a mountain. The altitude you reach depends only on your current position on the mountain, not on the winding trail you took to get there. Altitude is a state function. However, the total distance you walked or the energy you expended sweating up the trail heavily depends on the specific path you chose. Distance and effort are path functions.

### Analyzing the Setup

In our thermodynamic system, we are told that the system goes from state $A$ to state $B$, and the internal energy change is $40	ext{ kJ/mol}$. The problem then adds a twist: the system takes a **reversible path** to get to $B$, but returns to state $A$ via an **irreversible path**.

This is a classic trap designed to make you overthink. The words "reversible" and "irreversible" are thrown in to distract you.

### The Master Equation

Internal energy, denoted by $U$ (or sometimes $E$), is a fundamental **state function**. This means the change in internal energy, $\Delta U$, is defined strictly by the final and initial states:

$$\Delta U = U_{	ext{final}} - U_{	ext{initial}}$$

It does not matter if the path was reversible, irreversible, fast, slow, or completely chaotic. The change in internal energy from $A$ to $B$ is always $U_B - U_A$, and the change from $B$ back to $A$ is always $U_A - U_B$.

### Final Calculation

Because the system starts at state $A$, goes to state $B$, and then returns exactly to state $A$, the entire journey is a **cyclic process**. The initial state and the final state of the overall process are identical.

$$\Delta U_{	ext{net}} = U_A - U_A = 0$$

For any cyclic process, the net change in any state function (like internal energy, enthalpy, entropy, or pressure) is always exactly **zero**. The $40	ext{ kJ/mol}$ gained during the forward trip is perfectly lost during the return trip, regardless of the path's reversibility. Therefore, the net change in internal energy is zero.

Animated Solution for Chemistry - Chemical Thermodynamics: The internal energy change when a system goes from state $A$ to $B$ is $40 kJ/mol$ . If the system goes from $A$ to $B$ by a reversible path and returns to state $A$ by an irreversible path, what would be the net change in internal energy?

Select Answer:

Visualized Solution

\text{Visualizing the Process}

\text{Internal Energy as a State Function}

\text{Cyclic Process}

\text{Net Change in Internal Energy}

The Sigma Insight: First Law of Thermodynamics

The Magic of State Functions in Thermodynamics

Analyzing the Setup

The Master Equation

Final Calculation

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