What is the entropy change for an ideal gas during an isothermal expansion?

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Question: What is the entropy change for an ideal gas during an isothermal expansion?

Options:

Correct Answer: nR ln(Vf/Vi)

Solution:

The entropy change for an ideal gas during an isothermal expansion is ΔS = nR ln(Vf/Vi).

What is the entropy change for an ideal gas during an isothermal expansion?

What is the entropy change for an ideal gas during an isothermal expansion?

Step 1: Understand what isothermal means. Isothermal means that the temperature of the gas remains constant during the process.
Step 2: Know that entropy (S) is a measure of disorder or randomness in a system.
Step 3: Identify the variables: n is the number of moles of gas, R is the ideal gas constant, Vf is the final volume, and Vi is the initial volume.
Step 4: Recall the formula for entropy change (ΔS) during an isothermal process for an ideal gas: ΔS = nR ln(Vf/Vi).
Step 5: Recognize that ln is the natural logarithm, which is a mathematical function.
Step 6: To find the entropy change, plug in the values for n, R, Vf, and Vi into the formula.

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