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How do you convert $100\,\text{mm of Hg}$ to $Pa$?

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Last updated date: 23rd Jul 2024
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Answer
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Hint:The physical force exerted on an object is known as pressure. The force exerted per unit area is perpendicular to the surface of the materials. F/A is the fundamental pressure formula (Force per unit area). Pascals are the unit of pressure (Pa).Absolute, atmospheric, differential, and gauge pressures are the different types of pressures.

Complete step by step answer:
A millimetre of mercury is a manometric unit of pressure, formerly defined as the extra pressure produced by a one-millimetre-high column of mercury, and now defined as precisely 133.322387415 pascals. It is expressed in millimetres of mercury (mmHg) or millimetres of mercury (mm Hg).

Although not an SI unit, the millimetre of mercury is still routinely used in medicine, meteorology, aviation, and many other scientific fields.Let's solve this problem using the relationships mentioned below.
-1 atm equals 760 mmHg.
-1 atm equals 101,325 Pa.

To transform from one unit of measurement to another, dimensional analysis is the best method. Now bringing up the dimensional analysis problems. Quantity given multiplied by Conversion Factor equals quantity sought. Here, 100 mmHg is the given quantity.The relationships are given above as a conversion factor.
$Pa = \text{Quantity Sought}$
\[\therefore 100{\text{mmHg}} \times \dfrac{{1\;{\text{atm}}}}{{760{\text{mmHg}}}} \times \dfrac{{101,325Pa}}{{1\;{\text{atm}}}} = 1.33 \times {10^4}\;{\text{Pa}}\]

Hence, the $100\,\text{mm of Hg}$ is equal to $1.33 \times {10^4}\;{\text{Pa}}$.

Note:Evangelista Torricelli conducted experiments with mercury in the 17th century that enabled him to measure the presence of air. He'd dip a glass tube, closed at one end, into a bowl of mercury and lift the closed end up, leaving the open end submerged. The mercury's weight would drag it back, creating a partial vacuum at the far end. This confirmed his assumption that air/gas has mass and exerts energy on everything around it.