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A fixed amount of an ideal gas is to be doubled in volume by one of the following processes: (A) isothermal expansion, (B) adiabatic expansion, (C) free expansion in an insulated container, (D) isobaric (constant pressure) expansion. If E1, E2, E3, and E4 are the changes in average kinetic energy of the gas molecules for processes A, B, C, and D respectively, which relation is correct?
- E2 = E3
- E1 = E4
- E1 > E2
- E3 > E4
Correct answer: E1 > E2
Solution
For an ideal gas, average KE per molecule = (3/2)kT, so the change in average KE is proportional to change in temperature. Process A (isothermal): deltaT = 0, so E1 = 0. Process B (adiabatic): gas does work with no heat input, so T falls, E2 < 0. Process C (free expansion in insulated container): no work done, no heat exchanged, so for ideal gas internal energy (and T) is unchanged, E3 = 0. Process D (isobaric): from PV = nRT, doubling V at constant P doubles T, so E4 > 0. Therefore E1 = E3 = 0, E2 < 0, E4 > 0. This gives E1 > E2 as the correct relation.
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