What is the entropy change when 2 moles of an ideal gas are compressed isotherma

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Question: What is the entropy change when 2 moles of an ideal gas are compressed isothermally from volume V2 to V1?

Options:

Correct Answer: -R ln(V1/V2)

Solution:

The change in entropy for an isothermal compression is ΔS = nR ln(V1/V2). For 2 moles, ΔS = 2R ln(V1/V2), which is negative since V1 < V2.

What is the entropy change when 2 moles of an ideal gas are compressed isothermally from volume V2 to V1?

What is the entropy change when 2 moles of an ideal gas are compressed isothermally from volume V2 to V1?

Step 1: Understand that we are dealing with an ideal gas and the process is isothermal, meaning the temperature remains constant.
Step 2: Recall the formula for the change in entropy (ΔS) during an isothermal process: ΔS = nR ln(V1/V2).
Step 3: Identify the variables: n is the number of moles (which is 2), R is the ideal gas constant, V1 is the final volume, and V2 is the initial volume.
Step 4: Substitute the number of moles into the formula: ΔS = 2R ln(V1/V2).
Step 5: Recognize that since V1 is less than V2 (the gas is being compressed), the value of ln(V1/V2) will be negative.
Step 6: Conclude that the change in entropy (ΔS) will also be negative, indicating a decrease in entropy due to the compression.

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