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Question: How do you convert \(0.75atm\) to \(mm{\text{ Hg}}\)?...

How do you convert 0.75atm0.75atm to mm Hgmm{\text{ Hg}}?

Explanation

Solution

As we know that pressure is defined as the force which is applied perpendicular to the surface of an object per unit area. It is expressed in various SI units, for instance: pascals, atm, bar, torr, mm Hgmm{\text{ Hg}}, cm Hgcm{\text{ Hg}}and Nm−2N{m^{ - 2}}.

Complete step-by-step answer:
As we know that pressure can be expressed in various units and these expression can be shown as below:
1atm=1bar=760torr=760mmHg=76cmHg=105Pa=105Nm−21atm = 1bar = 760torr = 760mmHg = 76cmHg = {10^5}Pa = {10^5}N{m^{ - 2}}
Using the above relation between various pressure conditions we can convert one unit into another. Like we can convert atm into bar or atm into mm Hgmm{\text{ Hg}} and so on.
So, 1atm=760mmHg1atm = 760mmHg
0.75atm=x mmHg0.75atm = x{\text{ }}mmHg
x mmHg=760×0.751x{\text{ }}mmHg = \dfrac{{760 \times 0.75}}{1}
x=1013.33mmHgx = 1013.33mmHg
Thus, the correct answer is x=1013.33mmHgx = 1013.33mmHg.

Additional information:
Pressure is given by the formula in terms of force and area acting on a particular substance which is given as: p=FAp = \dfrac{F}{A}. It is a scalar quantity. The CGS unit of pressure is given as the barye (Ba) which is equivalent to the 1dyne cm−21dyne{\text{ }}c{m^{ - 2}}. The standard atmospheric pressure (atm) is approximately equivalent to the air pressure at sea level of Earth and it is given in terms of pascal as 1atm=101,325Pa1atm = 101,325Pa. Also, mercury is used to express pressure because mercury possesses the high density that allows a shorter column as well as water is used which is non-toxic and is easily available.

The deep sea divers use other units of pressure which are metre sea water (MSW) and foot sea water (FSW) and these standard units of pressure are used to expose the pressure in diving chambers as well as personal decompression computers. An MSW unit is defined as equivalent to 0.1bar0.1bar and the relation between them is given as 1MSW=0.1bar1MSW = 0.1bar.

Note: Always remember that mmHgmmHg or millimetre of mercury, centimetre of water and the inches of mercury are used to express the pressure in terms of height of a column in a pressure measuring equipment called manometer.