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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

(a) -500 J

(b) -505 J

(c) +505 J

(d) 1136.25 J
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Ans: (b) -505 J

Sol: $w = -P_{ext}ΔV = -2.5(4.50 - 2.50)$

$= - 5 L \text{ }atm = - 5 \times 101.325 J = - 506.625 J$

$ΔU = q + w$

As, the container is insulated, thus $q = 0$

Hence, $ΔU = w = - 506.625 J$

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