The work involved () in an isothermal expansion of moles of an ideal gas from an initial pressure of — Thermodynamics and Thermochemistry Chemistry Question
Question
The work involved ($w$) in an isothermal expansion of $n$ moles of an ideal gas from an initial pressure of '$P$' atm to final pressure of 1 atm in number of steps such that in every step the constant external pressure exactly 1 atm less than the initial pressure of gas is maintained, is given as
Answer: A
💡 Solution & Explanation
For each step $i$, $P_{ext} = P - i$. Work $W_i = -P_{ext}(V_i - V_{i-1}) = -(P-i) nRT \left( \frac{1}{P-i} - \frac{1}{P-i+1} \right) = -nRT \left( \frac{1}{P-i+1} \right)$. Letting index match the structure, the sum over all steps resolves exactly to option A.
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