A rectangular narrow U-tube has equal arm lengths and base length, each equal to $l$ . the vertical arms are filled with mercury up to $l / 2$ and then one end is sealed. By heating the enclosed gas all the mercury is expelled. If atmospheric pressure is $P_{0}$ , the density of mercury is $ρ$ and cross-sectional area is S, then[Neglect thermal expansion of glass and mercury]

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Work done by the gas against the atmospheric pressure is $\frac{5 l}{2} P_{0} S$

Work done by the gas against the gravity is $\frac{7}{4} S ρ g l^{2}$

Work done by the gas against the atmospheric pressure is $P_{0} S l$

Work done by the gas against the gravity is $S ρ g l^{2}$

answer is A, B.

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Detailed Solution

Total displacement of mercury against atmospheric process $= [l + \frac{l}{2} + l]$
$P E_{i n i t i a l} = [(ρ S \frac{l}{2}) \frac{l}{4}] \times 2 + 0$ {Assuming zero at ground level};

$P E_{\max} [(ρ S \frac{l}{2}) \times 2 + ρ S l] l$

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