How does Boyle's law relate to breathing?
The thoracic cavity that holds your lungs is fairly static as the rib cage is not flexible nor is there musculature to move the ribs. However, at the base of the ribcage is a large flat muscle called the diaphragm that separates the thoracic cavity from the abdominal cavity.
When the diaphragm relaxes the muscle is compressed upward which reduces the volume of the thoracic cavity increasing the pressure within the newly compressed space and creating a pump that forces air molecules from the lungs to travel up the bronchioles, into the bronchi, trachea, larynx and pharynx and exit the body through the nasal passages or the mouth if you standing slack jawed and open mouthed like a Neandrathal.
When the diaphragm contracts it pulls downward toward the abdominal cavity and expands the volume of the thoracic cavity. This in turns decreases the pressure in the lungs and creates empty space which forms a vacuum. This reduction in pressure pulls air into the lungs. That air can enter the respiratory tract from your nasal cavities or your neandrathal slack jawed open mouth, into the pharynx, larynx, trachea, bronchi, bronchioles and into the alveoli to diffuse oxygen and carbon dioxide.
It is the inverse relationship of Pressure and Volume of Boyle's Law that creates the pump - vacuum activity that allows for us to breathe.
YouTube video from SoCoolScienceShow
I believe the breathing explanation is incorrect.
Boyles Law: P1V1 = P2V2
"For a fixed mass of enclosed gas at a constant temperature, the production of pressure and volume remains constant."
This does not apply to non-pressure breathing. It only applies to enclosed spaces changing volume. When a piston in an engine is on the compression stroke- (i.e. valves closed) Boyles Law applies.
The only space where Boyles law applies with regard to breathing is the pleural cavity which is enclosed and therefore experiences changes of pressure/volume as the lungs expand and contract.
At rest, the lungs experience fluid flow with an increasing/decreasing volume but as they are open to the static atmosphere there are flow/mass changes not pressure/volume changes in the way that Boyles Law states.
A balloon rising up in the atmosphere and expanding is an example of Boyles Law because the balloon is sealed.
There is no gas flow in or out..
See the link here: https://www.youtube.com/channel/UCXbz7N6FrekxSCONMEhsz2w
Here's a nice worked example I found on Boyle's law and intrapulmonary and intrapleural pressures during breathing.
So, let's say we start with a lung volume of 2400 mL - this is called the functual residual capacity, and an intrapulmonary pressure equal to atmospheric pressure - 760 mmHg. Now a 500-mL breath is taken in, which will bring the volume of the lungs to 2900 mL.
If you set up the equation for Boyle's law, you'll have
Increase in volume, decrease in pressure. The calculated difference between
However, this is not what's measured; the actual drop in pressure is approximately 1 mmHg, and that until the pressure equalizes with the atmospheric pressure again.
So, volume is expanded, pressure drops and air starts flowing into the lungs; but the intrapulmonary pressure drop is nowhere near the value it would have had given an enclosed system.