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

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

Options:

  1. R ln(V2/V1)
  2. R (V2 - V1)
  3. R (V1/V2)
  4. 0

Correct Answer: R ln(V2/V1)

Solution: 

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

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

Practice Questions

Q1
What is the change in entropy when 1 mole of an ideal gas expands isothermally and reversibly from volume V1 to V2?
  1. R ln(V2/V1)
  2. R (V2 - V1)
  3. R (V1/V2)
  4. 0

Questions & Step-by-Step Solutions

What is the change in entropy when 1 mole of an ideal gas expands isothermally and reversibly from volume V1 to V2?
Correct Answer: ΔS = R ln(V2/V1)
  • Step 1: Understand that we are looking for the change in entropy (ΔS) when an ideal gas expands.
  • Step 2: Recognize that the process is isothermal, meaning the temperature remains constant during the expansion.
  • Step 3: Note that the process is reversible, which means it can be reversed without any net change in the system and surroundings.
  • Step 4: Recall the formula for the change in entropy for an ideal gas during isothermal and reversible expansion: ΔS = nR ln(V2/V1).
  • Step 5: Identify that 'n' is the number of moles of gas. In this case, we have 1 mole, so n = 1.
  • Step 6: Substitute n = 1 into the formula: ΔS = R ln(V2/V1).
  • Step 7: Recognize that R is the ideal gas constant, which is a known value.
  • Step 8: The final expression for the change in entropy when 1 mole of an ideal gas expands from volume V1 to V2 is ΔS = R ln(V2/V1).
  • Entropy Change in Ideal Gases – The concept of entropy change during isothermal and reversible processes for ideal gases, specifically focusing on the relationship between volume and entropy.
  • Isothermal Process – Understanding that the temperature remains constant during the expansion, which affects the calculation of entropy.
  • Reversible Process – Recognizing that the process is reversible, which allows the use of specific equations for calculating changes in state functions like entropy.
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