A manometer reads the pressure of a gas in a enclosure as shown in figure(a) When some of the gas is removed by a pump, the manometer reads as in (b). The liquid used in the manometers is mercury and the atmospheric pressure is `76 cm` of mercury.

(i) Give the absolute and gauge pressure of the gas in the enclosure for cases (a) and (b) in units of cm of mercury .
(ii) How would the level change in case (b) if `13.6 cm` of water are poured into the right limb of the manometer?

Explanation

The atmospheric pressure, `P=76cm` of mercury
(a). From figure (a)
pressure head, `h=20cm` of mercury
`therefore` absolute pressure `=p+h=76+20=96cm` of mercury
Also, gauge pressure `=h=20cm` of mercury
From figure (b),
Pressure head, `h=-18cm` of mercury
`therefore` Absolute pressure `=p+h=76+(-18)=58cm` of mercury
Also, gauge pressure `=h=-18cm` fo mercury
(b) When 13.6 cm of water is poured into the right limb of the manometer of figure (b),
then, using the relation
pressure `=rhogh=rho'g'h'`
we get `h'=(rhoh)/(rho')=(1xx13.6)/(13.6)=1cm` of mercury [`rho'`=density of mercury]
therefore, pressure at the point B,
`p_(B)=P+h'=76+1=77cm` of mercury
if `h''` is the difference in the mercury levels in the two limbs, then taking `P_(A)=P_(B)`
`implies58+h''=77implies77-58=19cm` of mercury