# How does the Ideal gas law relate to hot air balloons?

Jun 8, 2018

Recall,

$P V = n R T$

You're keeping the temperature of the air within the balloon higher than the temperature of the air outside of the balloon.

$\implies \frac{n}{V} = \rho \propto \frac{1}{T}$

In English that means we can prove based on the ideal gas law, that density and temperature of gases are inversely proportional.

To be even simpler, hot air will rise in cool air because its density is less. Hence, buoyancy.