Question related pressure. From AS LEVEL Physics. What will be the answer?

The density of air on the Earth decreases almost linearly with height from 1.22kgm–3 at sea level to 0.74 kgm–3 at an altitude of 5000m. Atmospheric pressure at the Earth’s surface on a particular day is 100000Pa. The value of g between the Earth’s surface and an altitude of 5000 m can be considered to have a constant value of 9.7ms–2. What will be the atmospheric pressure at an altitude of 5000m?

Oct 8, 2016

I found: $64110 P a$

Explanation:

Have a look: In my solution for reasons unknown (to me at least!) I used $\rho = 0.72 \frac{k g}{{m}^{3}}$ while the given value should be: $\rho = 0.74 \frac{k g}{{m}^{3}}$.
Using this given value in the formula for pressure you get:

$\textcolor{red}{{p}_{2} = 64110 P a}$

Dec 6, 2016

Alternate solution using Barometric formula.
Please note that all the given quantities are not used.

Explanation:

The relationship between the atmospheric pressure, temperature, and height is given as
${P}_{h} = {P}_{s} \times {e}^{- \frac{m g h}{k T}}$
where ${P}_{s}$ is atmospheric pressure at sea level, $h$ is height at which pressure is to be found, $g$ is acceleration due to gravity, $T$ is temperature of atmosphere in absolute scale; taken as constant, $k$ is Boltzmann's constant and $m$ is average atomic mass of air taken as $29 a m u$ Inserting various values, ${P}_{5000}$ can be found as $56570 P a$