What is the entropy change for a reversible isothermal expansion of an ideal gas

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Question: What is the entropy change for a reversible isothermal expansion of an ideal gas?

Options:

Correct Answer: nR ln(Vf/Vi)

Solution:

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

What is the entropy change for a reversible isothermal expansion of an ideal gas?

What is the entropy change for a reversible isothermal expansion of an ideal gas?

Step 1: Understand what entropy (S) is. It is a measure of disorder or randomness in a system.
Step 2: Recognize that an isothermal process means the temperature (T) remains constant during the expansion.
Step 3: Identify that a reversible process is one that can be reversed without any change in the surroundings.
Step 4: Know that for an ideal gas, the number of moles (n) and the gas constant (R) are important in calculating entropy change.
Step 5: Understand that Vf is the final volume and Vi is the initial volume of the gas.
Step 6: Use the formula for entropy change in a reversible isothermal expansion: ΔS = nR ln(Vf/Vi).
Step 7: Plug in the values of n, R, Vf, and Vi into the formula to calculate the entropy change.

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