Question

A $1pascal = 1N{m^{ - 2}}$ If mass of air at sea level is $1034gc{m^{ - 2}}$ , calculate the pressure in pascal.

Answer 1

Air is a mixture of various gases. Pressure is a physical quantity which refers to the physical force exerted on an object acting perpendicular to the object. Sea level is the base or standard level of measuring the elevation or depth of Earth. The pressure is calculated as the ratio of force to area.
Formula used: $\text{Pressure} = \dfrac{{Force}}{{Area}}$
and it is given to us that $1pascal = 1N{m^{ - 2}}$.

Complete step by step answer:
Air is a mixture of different gases in different compositions. Air contains 21% oxygen, 78% nitrogen and 1% other gases. The average molar mass of dry air is given by the sum of mole fractions of each gas multiplied by their molar mass. Air contains a certain amount of moisture or water vapours which depend on the capacity of air to hold them varying on the basis of the temperature.
Pressure is the physical force exerted on an object and it acts perpendicular to the surface of the object per unit area and is therefore, calculated as the ratio of force exerted on a surface to the area of the surface on which the force has been applied. Area is calculated in ${m^2}$ and since pressure is ratio of force and area therefore, pressure is calculated in $\dfrac{N}{{{m^2}}}$ and this unit of pressure is known as Pascal. $1Pa = 1N{m^{ - 2}}$ . Sea level is the base or standard level of measuring the elevation or depth of Earth.
For the given question, we know that
$\text{Pressure} = \dfrac{{Force}}{{Area}}$
It is given that the mass of air at sea level = $1034gc{m^{ - 2}}$
The force is calculated as $F = m \times g$
Where $m$ is the mass and $g$ is gravity and $g = 9.8m{s^{ - 2}}$
$P = \dfrac{F}{A}$
$\Rightarrow \dfrac{{1034g \times 9.8m{s^{ - 2}}}}{{c{m^2}}} \times \dfrac{{1kg}}{{1000g}} \times \dfrac{{100cm}}{{1m}}$
$\Rightarrow = 1.01332 \times {10^5}N$
$P = 1.013 \times {10^5}kg{m^{ - 1}}{s^{ - 2}}$
We know that,
$1pascal = 1N{m^{ - 2}}$
$1N = 1kgm{s^{ - 2}}$

$\text{Pressure} = 1.013 \times {10^5}Pa$

Note:
Differential pressure is the difference between two applied forces. It is represented as
$\Delta p$ . The most important type of pressure is the atmospheric pressure which is the weight of the atmosphere around us at a certain height. Here the absolute pressure is zero. Other types of pressure include absolute pressure and overpressure which is the pressure measured in the technological field.