Question

What is the appropriate mass of 1 cm² column of air that extends from sea level to the top of the atmosphere? A) 1 gB) 1 kgC) 10 kg D) 100 kg

Answer 1

The air pressure at sea level is about 0.1 MPa or 101000 Pa.

The pressure is given as,

`P=(F)/(A)`

Rearranging the above equation in order to get an expression for force,

`F=PA`

For the cossestion area of 1 square centimeter, the force is given as,

`\begin{gathered} F=101000\text{ Pa}*(1\text{ cm})^2 \\ =101000\text{ Pa}*(0.01\text{ m})^2 \\ =101000\text{ Pa}*0.0001m^2 \\ =10.1\text{ N} \end{gathered}`

The force is give as,

`\begin{gathered} F=ma \\ =mg \end{gathered}`

Here, g is the acceleration due to gravity .

Rearranging the above equation in order to get mass,

`m=(F)/(g)`

Substituting all known values,

`\begin{gathered} m=\frac{10.1\text{ N}}{(10ms^(-2))^{}} \\ =1.01\text{ kg} \\ \cong1\text{ kg} \end{gathered}`

Therefore, the appropriate mass of 1 square centimeter column of air that extends from sea level to the top of atmosphere is 1 kg. Hence, option (b), is the correct choice.