# How does Charle's law relate to breathing?

Jan 1, 2014

It affects the volume of air you can inhale.

#### Explanation:

Charles’ Law is

$\textcolor{b l u e}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} {V}_{1} / {T}_{1} = {V}_{2} / {T}_{2} \textcolor{w h i t e}{\frac{a}{a}} |}}} \text{ }$

This means that, when you inhale cold air, it will change volume as it warms in passing through the sinuses.

As the air warms it expands to a larger volume.

Charles’ Law does not affect breathing nearly as much as Boyle’s Law does, but it does have an effect.

Assume that each time you breathe, you inhale and exhale about 500 mL of air.

If it is a cold day with a temperature of -10 °C, the inhaled air will expand as it reaches the temperature in your lungs (37 °C). What volume of cold air would you have to inhale to make a volume of 500 mL at 37 °C?

V_2 = V_1 × T_2/T_1 = "500 mL" × (263 color(red)(cancel(color(black)("K"))))/(310 color(red)(cancel(color(black)("K")))) = "420 mL"

You take shorter breaths in winter to account for the increased volume of inspired air.

On a hot summer day (37 °C), the air temperature is the same outside as inside your lungs. You would be inhaling 500 mL of air.