Give the absolute and gauge pressure of the gas in the enclosure for cases (a) and (b)in units of cm of mercury.

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Solution

Case (a) :
Difference in the height of the mercury levels $= 20$ cm
$∴$ Gauge pressure $= ρ g h = ρ g (20)$
Thus gauge pressure is $20$ cm of mercury.

Also $P_{A} = P_{B} + ρ g h$
$∴$ $P_{A} = P_{o} + ρ g (h) = ρ g (76) + ρ g (20) = ρ g (96)$
$⟹$ Absolute pressure is $96$ cm of mercury.

Case (b) :
Difference in the height of the mercury levels $= 18$ cm
$∴$ Gauge pressure $= ρ g h = ρ g (18)$
Thus gauge pressure is $18$ cm of mercury.

Also $P_{Q} = P_{P} + ρ g h$
$∴$ $P_{P} = P_{o} - ρ g (h) = ρ g (76) - ρ g (18) = ρ g (58)$
$⟹$ Absolute pressure is $58$ cm of mercury.

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