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Ideal Gas Equation

If w1, w2, ...

Question

If $w_{1}, w_{2}, w_{3}, w_{4}$ for an ideal gas are magnitude of work done in isothemal, adiabatic, isobaric, isochoric reversible expansion processes. (assume expansion to be from same initial points to same final volume wherever applicable) The correct order will be :

A

w_{1} > w_{2} > w_{3} > w_{4}

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B

w_{3} > w_{2} > w_{1} > w_{4}

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C

w_{3} > w_{2} > w_{4} > w_{1}

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D

w_{3} > w_{1} > w_{2} > w_{4}

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Solution

The correct option is D $w_{3} > w_{1} > w_{2} > w_{4}$
Isothermal vs. Adiabatic process:
The isothermal curve lies above the adiabatic curve in the p-v diagram. Hence, work done in the isothermal process is greater than that in an adiabatic process
$w_{1} > w_{2}$
Both $w_{1}$ and $w_{2}$ are > 0.

Isochoric Process:
Since v=constant, work done is zero.
$W = \int_{v_{1}}^{v_{2}} P d V = 0$ since dV is zero
$w_{4} = 0$
Isobaric Process:
$w_{3} = P (V_{2} - V_{1})$
$w_{3} > 0$
Since initial pressure remains constant max work will be done in this case.

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