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Question

# The figure here shows five paths traversed by a gas on a P-V diagram. Rank the paths according to the change in internal energy of the gas, greatest first.

A

5 > 4 = 3 > 2 = 1

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B

5 > 4 = 3 > 1 = 2

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C

4 = 3 > 5 > 1 = 2

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D

5 > 4 = 3 = 2 = 1

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Solution

## The correct option is D 5 > 4 = 3 = 2 = 1 For any ideal gas, the internal energy can be related to the temperature as - Eint = nCvT ⇒ ΔEint = nCvΔT (for a change of state). Thus the change in internal energy is solely dictated by the change in temperature.Since, all the processes 1, 2, 3, and 4 begin and end at the same temperatures, their Δ T′s (and, Δ Eint = nCv(T2 − T1)) are the same. Process 5, on the other hand goes through a larger Δ T(T3−T1), hence gains the highest internal energy.

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