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Question: How is \(101325N{{m}^{2}}\) or Pascal is derived? Explain simply....

How is 101325Nm2101325N{{m}^{2}} or Pascal is derived? Explain simply.

Explanation

Solution

Atmospheric pressure is the pressure exerted by the air. It can be calculated using different units but its standard value is taken as 101325Nm2101325N{{m}^{2}}. The atmospheric pressure can also be calculated as equivalent to the pressure exerted by a column of mercury. The pressure is equal to the force exerted divided by total surface area.

Complete solution:
The atmospheric pressure is the pressure exerted by the blanket of atmosphere on the Earth’s surface. The standard value of atmospheric pressure is 101325Nm2101325N{{m}^{2}}.
101325Nm2=760Torr101325N{{m}^{2}}=760Torr
We know that, 1Torr≈1mm Hg1Torr\approx 1mm\,Hg
Therefore,
101325Nm2=760mm Hg101325N{{m}^{2}}=760mm\,Hg

The weight of 760mm760mm bar of Hg will be-
W=mgW=mg
Here, WW is the weight of column of Hg
mm is the mass of the column
gg is acceleration due to gravity

From the above equation, we have,
W=mg ⇒W=ρ×V×g \begin{aligned} & W=mg \\\ & \Rightarrow W=\rho \times V\times g \\\ \end{aligned}
Here, ρ\rho is the density
VV is the volume

For mercury, ρ=13595.08kg m−3\rho =13595.08kg\,{{m}^{-3}}, V=760×10−3×unit areaV=760\times {{10}^{-3}}\times unit\,area
We substitute given values in the above equation to get,
W=760×10−3×13595.08×10 W=101324.87N \begin{aligned} & W=760\times {{10}^{-3}}\times 13595.08\times 10 \\\ & W=101324.87N \\\ \end{aligned}

Therefore, the weight of 760mm760mmHg is 101324.87N101324.87N
We know that,
P=WAP=\dfrac{W}{A}
Here, PP is the pressure
AA is the area of cross section
Therefore,
P=101324.87unit area ⇒P=101324.87P \begin{aligned} & P=\dfrac{101324.87}{unit\,area} \\\ & \Rightarrow P=101324.87P \\\ \end{aligned}

Therefore, the pressure of 760mm760mm Hg is approximately equal to the standard atmospheric pressure.

Hence, the atmospheric pressure is calculated from the column of Hg bar.

Note:
The pressure of the Earth’s atmosphere at mean sea level is taken as 1 atm. Mm Hg is a unit of pressure which is equal to the pressure exerted by mercury which is 1mm high. The SI unit of pressure is Pascal and the CGS unit is Torr. As we go at greater altitudes, the blanket of air gets thinner and hence pressure increases and vice versa.