What is the change in entropy when 1 mole of an ideal gas expands isothermally f

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Question: What is the change in entropy when 1 mole of an ideal gas expands isothermally from volume V1 to V2?

Options:

Correct Answer: R ln(V2/V1)

Solution:

The change in entropy for an isothermal expansion of an ideal gas is given by ΔS = nR ln(V2/V1). For 1 mole, it simplifies to ΔS = R ln(V2/V1).

What is the change in entropy when 1 mole of an ideal gas expands isothermally from volume V1 to V2?

What is the change in entropy when 1 mole of an ideal gas expands isothermally from volume V1 to V2?

Step 1: Understand that entropy (S) is a measure of disorder or randomness in a system.
Step 2: Recognize that we are dealing with an ideal gas that is expanding isothermally, meaning the temperature remains constant during the process.
Step 3: Identify that we have 1 mole of gas, which simplifies our calculations since we can use the value of n (number of moles) as 1.
Step 4: Recall the formula for the change in entropy (ΔS) during an isothermal expansion of an ideal gas: ΔS = nR ln(V2/V1).
Step 5: Substitute n = 1 into the formula, which gives us ΔS = R ln(V2/V1).
Step 6: Recognize that R is the ideal gas constant, approximately equal to 8.314 J/(mol·K).
Step 7: Understand that V1 is the initial volume and V2 is the final volume after expansion.
Step 8: Calculate the natural logarithm of the ratio of the volumes (ln(V2/V1)).
Step 9: Multiply the result by the gas constant R to find the change in entropy (ΔS).

Entropy Change in Isothermal Processes – The concept of entropy change during an isothermal expansion of an ideal gas, which is calculated using the formula ΔS = nR ln(V2/V1).
Ideal Gas Behavior – Understanding the properties of ideal gases and how they behave under isothermal conditions.