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. $${\displaystyle \frac{F}{A}}$$. 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 ($$1m^2$$). So, the force exerted on this surface is pressure. Because,
 $$P(pressure)={\displaystyle \frac{F}{A}}$$ , if we put value of$$A=1m^2$$,
 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, $$1m^2\to 10340kg$$
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.