Question

Pressure is determined as force per unit area of the surface. The SI units of pressure, pascal is as shown below:
$1Pa=1N{{m}^{-2}}$
If the mass of air at sea level is 1034 g, calculate the pressure in pascal.

Answer 1

Hint: We know that Pascal is the SI unit of pressure, which is $N/{{m}^{2}}$. And pressure is the force applied per unit area or the weight per unit area.

Complete step-by-step answer:
It is given that pressure is force per unit area by any liquid, gas or solid i.e. $\dfrac{F}{A}$. And the SI unit of pressure is pascal ($N/{{m}^{2}}$=$kgm/{{\sec }^{2}}$).
Let’s assume there is one surface at sea level of the unit area ($1{{m}^{2}}$). So, the force exerted on this surface is pressure. Because,
$P(pressure)=\dfrac{F}{A}$ , if we put value of$A=1{{m}^{2}}$,
Then, $P=F$.
And it is given that at sea level pressure is due to air. Force at the surface of sea level $F=mg$ and $P=F$. And given that mass of $1c{{m}^{2}}\to 1034g,$
${{10}^{-4}}{{m}^{2}}\to 1034g$
Then for, $1{{m}^{2}}\to 10340kg$
So, the force $F=(10340kg)\times (9.8m{{\sec }^{-2}})$
=101,332 N
$P$ = 101,332 $N{{m}^{-2}}$
= 101,332 $Pa$
$P$=$1.01332\times {{10}^{5}}Pa$, this is the standard atmospheric pressure at sea level.
1atm = $1.01332\times {{10}^{5}}Pa$

Note: Here, we will take the standard value of gravity (g) = $9.8m{{\sec }^{-2}}$ not $10m{{\sec }^{-2}}$. Pressure decreases as the altitude or height from the sea level increases from the sea level.