From centimetres of mercury to pascals
"76 cm Hg" can be read as a pressure, but it is not a unit of pressure — it is a height. P = hρg converts it into pascals.
The problem
At sea level atmospheric pressure is 76 cm Hg. Taking the density of mercury as 13 600 kg m−3 and the acceleration due to gravity as 10 m s−2,
(i) find the atmospheric pressure in Pa.
(ii) find the height of the water column that atmospheric pressure can balance. (density of water 1000 kg m−3)
Solution (i)
atmospheric pressure = h × ρ × g
P = (76 ÷ 100) m × 13 600 kg m−3 × 10 m s−2
= 103 360 Pa
Solution (ii)
If the height of the water column is h, it must produce that same pressure.
h ρ g = 103 360
h × 1000 × 10 = 103 360
h = 103 360 ÷ 10 000
h = 10.336 m
Why mercury is used
To produce the same pressure, water needs a column over 10 metres tall, while mercury needs only 76 centimetres. The reason is that mercury is 13.6 times as dense as water — so the height needed for the same pressure is 13.6 times smaller.
The value at sea level
The standard value of atmospheric pressure at sea level is 76 cm Hg — that is, the pressure produced by a mercury column 76 cm high, which in pascals is about 103 360 Pa.