Question

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

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

2. How would the levels change in case of (b) if 13.6 cm of water (immiscible with mercury) are poured into the right limb of the manometer? (Ignore the small change in the volume of the gas).

Answer 1

1. Difference between the mercury levels in the two limbs gives gauge pressure

∴ Gauge pressure, P_a = 20 cm of mercury

Atmospheric pressure, P_o = 76 cm of mercury

∴ Absolute pressure = Atmospheric pressure + Gauge pressure 

= 76 cm + 20 cm

= 96 cm of mercury

2. Difference between the levels of mercury in the two limbs = – 18 cm

∴ Gauge pressure = – 18cm of mercury

∴ Absolute pressure = Atmospheric pressure + Gauge pressure

= 76cm – 18 cm 

= 58 cm of mercury.