Physics Applied to Diving 5.- Ideal Gas Model

The ideal gas model shows the relationships between the pressure, volume, amount of substance, and temperature of a gaseous system. This model is commonly express by the next equation:

PV = nRT

Where P is pressure, V is volume, n is the amount of substance, T is the absolute temperature and R is the ideal gas constant with value of 0.082 [L atm/mol K]. This is not the most exact model we have today, but it's quite useful for simple calculations and to understand the phenomena of gaseous systems in our diving activities. To understand this model, we must acknowledge 5 assumptions it does first [1]:

1.- The number of molecules in the gas is large, and the average separation is large compared with their dimensions.

2.- The molecules obey Newton's law of motion, but they move randomly.

3.- The molecules interact only through short-range forces during elastic collisions.

4.- The molecules make elastic collisions with the walls.

5.- All molecules in the gas are identical.

Mainly what the assumptions express is that this model may not be useful in extreme scenarios. The good thing is that the places we can survive in, are far from this scenario so we shouldn't have any problem using this model for our purposes. This equation results from the combination of 4 empirical laws which have the name of their inventors: Boyle's Law, Charles's law, Gay-Lussac's Law and Avogadro's Law. These laws can be found inside the equation of the ideal gas model like shown in the image.

Calculations

This equation can be used to determine the value of the pressure, volume, temperature or amount of substance of a gaseous system whenever we have 3 of the four variables by doing a simple clearance.

Example. - What’s the volume?

If we have a gaseous system with a temperature of 30 °C, a pressure of 1 atm and an amount of substance of 4 mol, how much volume does it has?

What we know:

T = 30°C

P = 1 atm

n = 4 mol

R = 0.082 L atm / mol K

V = ?

The first thing we must do is to transform the temperature unites to absolute unites. In this case we are going to use Kelvin units so:

T = 30 °C = (30 + 273.15) K= 303.15 K

After we have the same units of pressure, volume and amount of substance between the variables we are going to use, we can make an easy calculation:

PV = nRT

V = nRT / P

V = (4 mol)(0.082 L atm / mol K)(303.15 K) / 1 atm

V = 99.43 L

[1] Raymond A. Serway, College Physics, CENEGAGE learning, eights edition, 2009, page 340

April 05, 2020 Tags : All , Book , Physics Applied to Diving

Sunday, April 5, 2020

Physics Applied to Diving 5.- Ideal Gas Model