A gas present in a cylinder, fitted with a frictionless piston, expands against a constant pressure of 1 atm from a volume of 2 litre to a volume of 6 litre. In doing so, it absorbs 800 J heat from surroundings. The increase in internal energy of process is

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305.85 J

405.83 J

-463.28 J

394.95 J

answer is B.

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Detailed Solution

Work is done against constant pressure and thus, irreversible.
Given, $ΔV = 6 - 2 = 4 L and p = 1 atm$
From first law of thermodynamics,
$\begin{array}{l} W = - p \times dV \\ = 1 \times 4 Latm FrO1 \\ = \frac{1 \times 4 \times 1 .987}{0 .0821} cal \\ (∵ 0 .0821 Latm = 1 .987 cal) \\ = 96 .81 cal \\ = - 96 .81 \times 4 .184 J = - 405 .04 J \\ q = ΔE - W \\ ΔE = q + W = 800 + (- 405 .04) \\ = 394 .95 J \end{array}$

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