Question

$1Pa = 1N{m^{ - 2}}$
If the mass of air at sea level is $1034gc{m^{ - 2}}$ , calculate the pressure in pascal.
(A) $101 \times {10^5}Pa$
(B) $1Pa$
(C) $1.0133 \times {10^5}Pa$
(D) $10133 \times {10^5}Pa$

Answer 1

$1N = 1Kgm{s^{ - 2}}$ Using this conversion one can relate it with the given value which is in grams. The value in Pascal will be higher.

Complete step by step solution:
The force applied in a perpendicular direction to the surface of an object per unit area is said to be the pressure applied.
The formula of pressure: When force (F) is applied perpendicularly to a particular area (A), then the pressure experienced by the surface of the object will be the ratio of force and area. Thus the formula for pressure will be as follows:
$P = \dfrac{F}{A}$
From the equation we can see that pressure is directly proportional to the force applied and inversely proportional to the surface area of the object. This means that more the force applied, more will be the pressure experienced. Smaller the surface area, larger will be the pressure experienced.
Units of Pressure: There are different units of pressure. If we assign the units with respect to the formula then the unit will be as follows:
$P = \dfrac{F}{A} = \dfrac{N}{{{m^2}}}$
Force is measured in Newton and the area of the object has the unit ${m^2}$. So accordingly the unit of pressure will be $N{m^{ - 2}}$. This unit was given by Pascal therefore, is also called Pascal. $\therefore 1Pa = 1N{m^{ - 2}}$
Calculation of Pressure of the air at sea level:
The only given data is the mass of air at sea level is $1034gc{m^{ - 2}}$ . We have the formula for Pressure which is $P = \dfrac{F}{A}$
We can further reduce the formula by substituting the value of force. Force is the product of mass and acceleration.
$F = m \times g$
Here the acceleration will be due to gravity (g), which is given by $9.8m/{s^2}$
So we can calculate force as follows:
$F = 1.034Kg \times 9.8m{s^{ - 2}}$
$F = 10.143Kgm{s^{ - 2}} = 10.143N$
The value of area is $1c{m^2} = 1 \times {10^{ - 4}}{m^2}$
Substituting the values of force and area in the formula of pressure we get,
$P = \dfrac{{10.143N}}{{1 \times {{10}^{ - 4}}{m^2}}}$
$P = 10.133 \times {10^4}N{m^{ - 2}} = 1.0133 \times {10^5}N{m^{ - 2}}$.
We know that $1Pa = 1N{m^{ - 2}}$
$\therefore P = 1.0133 \times {10^5}Pa$

So, the option (C) is the correct one.

Note: Here the sign of acceleration due to gravity should be positive as the acceleration is directed in downward direction. Also all the units should be first converted to the SI system before calculations.