https://file.aiquickdraw.com/mathbot/file/17254674609696d8dg1m0.jpg

The image contains a problem related to thermodynamics, specifically focusing on entropy changes for different thermodynamic processes.

### Problem Statement:
The problem seems to be asking about the entropy change (ΔS) of 2 moles of an ideal gas undergoing a reversible isothermal expansion at a temperature of 298 K from an initial volume \( V_i \) to a final volume \( V_f \).

### Relevant Formula:
For a reversible isothermal process, the entropy change is given by:
\[
\Delta S = nR \ln\left(\frac{V_f}{V_i}\right)
\]
where:
- \( n \) is the number of moles of the gas,
- \( R \) is the universal gas constant (approximately 8.314 J/mol·K),
- \( V_f \) is the final volume,
- \( V_i \) is the initial volume.

### Answer Options:
The image appears to list multiple-choice answers. Unfortunately, the exact volumes \( V_i \) and \( V_f \) are not visible, which are necessary to solve for the entropy change.

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To solve the problem:
1. Identify the values of \( V_i \) and \( V_f \) (likely provided in the question but not visible).
2. Substitute the values into the entropy change formula.
3. Calculate the entropy change.

### Example Calculation:
If the initial and final volumes were, for instance, \( V_i = 1 \, \text{L} \) and \( V_f = 2 \, \text{L} \), then:
\[
\Delta S = 2 \times 8.314 \times \ln\left(\frac{2}{1}\right) = 2 \times 8.314 \times \ln(2) \approx 11.53 \, \text{J/K}
\]

Would you like to provide the specific values of \( V_i \) and \( V_f \), or should I assist with something else related to this problem? 

#### Questions:
1. What is the relationship between entropy change and volume change in an isothermal process?
2. How does the number of moles of a gas affect the entropy change in a system?
3. What assumptions are made when calculating entropy change using the provided formula?
4. How would the entropy change differ for an adiabatic process?
5. What role does temperature play in determining the entropy change?

#### Tip:
Always check whether the process is reversible

The problem involves calculating the entropy change (ΔS) of 2 moles of an ideal gas undergoing a reversible isothermal expansion at a temperature of 298 K from an initial volume Vi to a final volume Vf.

This problem explores the entropy change (ΔS) for 2 moles of an ideal gas during a reversible isothermal expansion at 298 K. Learn how to use the entropy change formula ΔS = nR ln(Vf/Vi) with example calculations. Suitable for students in Grades 11-12 or college level.

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