How much work is performed when an ideal gas undergoes free expansion into an evacuated chamber (vacuum) under isothermal conditions?
Answer and explanation
Correct answer: D. Zero work
- Step 1: Mechanical expansion work against an external pressure is defined as .
- Step 2: In free expansion into a vacuum, there is no opposing external force, so .
- Step 3: Therefore, .
- Step 4: Because an ideal gas expands into a vacuum without doing work, and for an isothermal process of an ideal gas, no heat is absorbed ().
Answer
Zero work (w = 0)
Why not the others: 'w = -2.303 nRT log(V2 / V1)' is the formula for reversible isothermal expansion against a continuous opposing pressure, not a vacuum; 'w = -Pext * ΔV' is the general formula for expansion against constant non-zero external pressure; 'w = n Cv ΔT' is the formula for adiabatic work.
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