# Why does the density of gas in a hot air balloon decrease as the gas is heated?

Jun 24, 2017

The density $d$ of a gas is related by the equation

$d = \frac{M P}{R T}$

where

• $M$ is the molar mass of the gas (in $\text{g/mol}$)

• $P$ is the pressure of the gas (in $\text{atm}$)

• $R$ is the universal gas constant, equal to $0.082057 \left(\text{L"·"atm")/("mol"·"K}\right)$

• $T$ is the absolute temperature of the gas (in $\text{K}$)

We can see from this relationship that the density ($d$) of a gas and its temperature ($T$) are inversely proportional. That is, if the gas in the balloon is heated (temperature increased), its density will decrease (assuming relatively constant pressure).