What is the change in entropy when 1 mole of an ideal gas expands isothermally and reversibly from volume V1 to V2?
Practice Questions
1 question
Q1
What is the change in entropy when 1 mole of an ideal gas expands isothermally and reversibly from volume V1 to V2?
R ln(V2/V1)
R (V2 - V1)
R (V1/V2)
0
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).
Questions & Step-by-step Solutions
1 item
Q
Q: What is the change in entropy when 1 mole of an ideal gas expands isothermally and reversibly from volume V1 to V2?
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).
Steps: 8
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).
