What is the entropy change for the isothermal expansion of an ideal gas from vol

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Question: What is the entropy change for the isothermal expansion of an ideal gas from volume V1 to V2 at temperature T?

Options:

Correct Answer: R ln(V2/V1)

Solution:

The entropy change for an isothermal expansion is given by ΔS = nR ln(V2/V1). For 1 mole, ΔS = R ln(V2/V1).

What is the entropy change for the isothermal expansion of an ideal gas from volume V1 to V2 at temperature T?

What is the entropy change for the isothermal expansion of an ideal gas from volume V1 to V2 at temperature T?

Step 1: Understand that we are looking for the change in entropy (ΔS) when an ideal gas expands isothermally (at constant temperature).
Step 2: Identify the initial volume (V1) and the final volume (V2) of the gas.
Step 3: Recognize that the formula for the change in entropy for an isothermal process is ΔS = nR ln(V2/V1), where n is the number of moles and R is the ideal gas constant.
Step 4: If we are considering 1 mole of gas, we can simplify the formula to ΔS = R ln(V2/V1).
Step 5: Calculate the natural logarithm of the ratio of the volumes (V2/V1).
Step 6: Multiply the result by the ideal gas constant R to find the change in entropy (ΔS).

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