Question

The air density at Mount Everest is less than that at sea level. It is found by mountain for one trip lasting a few hours, the extra oxygen needed by them correspond to 30000 cc sea level (pressure $=1$ atmosphere, temperature $=27^{\circ} C$ )
Assuming that the lens around Mount Everest is $-73^{\circ} \mathrm{C}$ and that the oxygen cylinder has a capacity of 5.2 liters. The pressure at which oxygen be filed (at sire) in the cylinder is

Answer 1

Hint: We know that for a fixed mass of an ideal gas kept at a fixed temperature, pressure and volume are inversely proportional. Or Boyle's law is a gas law, stating that the pressure and volume of a gas have an inverse relationship. If volume increases, then pressure decreases and vice versa, when the temperature is held constant. Decreasing the volume of a gas increases the pressure of the gas. More collisions mean more force, so the pressure will increase. When the volume decreases, the pressure increases. This shows that the pressure of a gas is inversely proportional to its volume.

Complete step by step answer
To solve this, we can recall the concept that the pressure exerted by a static fluid depends only upon the depth of the fluid, the density of the fluid, and the acceleration of gravity. The fluid pressure at a given depth does not depend upon the total mass or total volume of the liquid. The pressure exerted by a column of liquid of height h and density $\rho$ is given by the hydrostatic pressure equation $p=~\rho gh$, where $\mathrm{g}$ is the gravitational acceleration.
We know that it is given that,
Volume $\mathrm{V}_{1}=30000 \mathrm{cc}$
Volume $\mathrm{V}_{2}=5200$
Pressure $\mathrm{P}_{1}=1$ atm
We know that, $\dfrac{\mathrm{P}_{1} \mathrm{V}_{1}}{\mathrm{T}_{1}}=\dfrac{\mathrm{P}_{2} \mathrm{V}_{2}}{\mathrm{T}_{2}}$
After we put the values in the above expression, we get:
$\dfrac{1 \times 30000}{300}=\dfrac{\mathrm{P}_{2} \times 5200}{200}$
$\mathrm{P}_{2}=3.85 \mathrm{atm}$

Hence, the pressure is 3.85 atm

Note: We know that since pressure x volume remains constant, for example, doubling the pressure on an enclosed gas will reduce its volume to 1/2 its previous size. Tripling the pressure will reduce its volume to 1/3, and so on. Alternatively, if we double the volume available to an enclosed gas, pressure is halved. The Temperature-Volume Law states that the volume of a given amount of gas held at constant pressure is directly proportional to the Kelvin temperature. As the volume goes up, the temperature also goes up, and vice-versa. Atmospheric pressure is an indicator of weather. When a low-pressure system moves into an area, it usually leads to cloudiness, wind, and precipitation. High-pressure systems usually lead to fair, calm weather. A barometer measures atmospheric pressure, which is also called barometric pressure.