Question

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

Answer 1

Hint: Atmospheric pressure is the pressure exerted by the air. It can be calculated using different units but its standard value is taken as $101325N{{m}^{2}}$. 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 $101325N{{m}^{2}}$.
$101325N{{m}^{2}}=760Torr$
We know that, $1Torr\approx 1mm\,Hg$
Therefore,
$101325N{{m}^{2}}=760mm\,Hg$

The weight of $760mm$ bar of Hg will be-
$W=mg$
Here, $W$ is the weight of column of Hg
$m$ is the mass of the column
$g$ is acceleration due to gravity

From the above equation, we have,
$\begin{align}
  & W=mg \\
 & \Rightarrow W=\rho \times V\times g \\
\end{align}$
Here, $\rho $ is the density
$V$ is the volume

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

Therefore, the weight of $760mm$Hg is $101324.87N$
We know that,
$P=\dfrac{W}{A}$
Here, $P$ is the pressure
$A$ is the area of cross section
Therefore,
$\begin{align}
  & P=\dfrac{101324.87}{unit\,area} \\
 & \Rightarrow P=101324.87P \\
\end{align}$

Therefore, the pressure of $760mm$ 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.