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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 $\Delta U$ of the gas in joules will be
Explanation
Insulated means q = 0, so $\Delta U = -P_{ext}\Delta V$.
Detailed Solution
$\Delta U = q + w$
For an adiabatic process, q = 0, so $\Delta U = w$
$w = -P\Delta V = -2.5\ atm\times(4.5 - 2.5)$ L
$= -2.5\times2$ L-atm $= -5\times101.3$ J
$= -506.5$ J $\approx -505$ J