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Question

The height of mercury column in a barometer in a Calcutta laboratory was recorded to be 75 cm. Calculate this pressure in SI and CGS units using the following data : Specific gravity of mercury = 13.6, Density of water =103kg/m3,g=9.8m/s2 at Calcutta.Pressure=hpg in usual symbols.

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Solution

Height of the Mercury Column in a Barometer = 75 cm.

For Finding the Pressure in S.I. System, Changing 75 cm into meter.

∴ Height of the Mercury column(h) = 75 cm.
= 0.75 m.

Acceleration due to gravity(g) = 9.8m/s2
Density of the Water =103kg/m3.
=1000kg/m3
Specific Gravity of the Mercury = 13.6

Specific Gravity of the Substance is the Ratio of the Density of the Substance to the Density of the Water.

∴ Specific Gravity = Density of the Substance /Density of the Water.
⇒ Density of the Mercury(ρ) = 1.3×1000
= 1300kg/m3.


Now,
Using the Formula,
Pressure(P) = hρg
= 0.75×1300×9.8
= 9555 Pa.

Hence, the Pressure is 9555 Pa.


For Finding the Pressure in C.G.S. System,

Height of the Mercury Column(h) = 75 cm.
Acceleration due to gravity(g) = 9.8m/s2
=9.8×100cm/s2
=980cm/s2.

Density of the Water =1000kg/m3.
= 1000×106g/106cm3.
= 106/106g/cm3.
= 1g/cm3

∴ Density of the Mercury(ρ) = Specific Gravity of the Mercury × Density of the Water.
=1.3×1
=1.3g/cm3.


Now Using the Formula,

Pressure(P)= hρg
= 75×1.3×980
= 9550 Ba.


Hence the Pressure is 9550 barye.



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