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A gas is allowed to expand in a well insulated container against a constant external pressure of 2.5 atm from an initial volume of 2.50 L to a final volume of 4.50 L. The change in internal energy ΔU of the gas in joules will be:

1. -500 J
2. -505 J
3. 1136.25 J
4. +505 J

Correct answer: -505 J

Solution

The process is adiabatic (well-insulated), so q = 0. Using the first law of thermodynamics, ΔU = q + w. Work done (w) = -P_ext × ΔV = -2.5 atm × (4.50 L - 2.50 L) = -2.5 × 2.00 L = -5.00 L·atm. Converting to joules: -5.00 × 101.325 = -505 J. Thus, ΔU = -505 J.

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