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.