Question

What is the pressure inside a system when the system-side column in an open mercury manometer is 75.0 mm lower than the atmosphere side when the atmospheric pressure is 735 mm hg?

Answer 1

Pressure can be measured using a U-tube manometer by measuring the difference of the height readings. The equation is equal to:

ΔP = ρgΔh
where
ΔP is the difference of pressure between gauge and atmospheric
ρ is the fluid used in manometer which is mercury (13,560 kg/m³)
g is 9.81 m/s²
Δh is the difference in height readings
The conversions is 101325 Pa = 760 mmHg


P - 760 mmHg = (13,560 kg/m³)*(9.81 m/s²)*(75 mm)*(1 m/1000 mm) * (760 mmHg/101325 Pa)
P = 834.83 mmHg

Answer 2

The pressure inside a system = 810 mmHg = 108 kPa

Further explanation

The pressure on the gas in a confined space is measured using a manometer. One that is used is an open manometer

The manometer is open in the shape of a U tube and is filled with mercury liquid with both ends open. The other end is related to external pressure while the other end is connected to the room where the pressure will be measured

The height of the mercury will change when the end of the tube is connected to the room

The equation used is

$\large{\boxed{\bold{P_{gas}~=~P_{bar}~\frac{+}{-}~h}}}$

P bar = atmospheric pressure

h = difference in mercury height

The + sign if the mercury surface at the tip associated with the outside air is higher and vice versa, the sign - if the mercury surface is lower

The statement of the question states that the surface/mercury level at the end connected to the system/room is lower than the open end, by 75 mm, so the amount of gas pressure:

P gas = P bar + h

P gas = 735 mmHg + 75 mm

P gas = 810 mmHg

P gas = 810 mmHg x 0.1333 kPa

P gas = 107.97 = 108 kPa

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Keywords: manometer, gas pressure, mercury, U tube