Question

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

Answer 1

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

`d = (MP)/(RT)`

where

• `M` is the molar mass of the gas (in `"g/mol"`)

• `P` is the pressure of the gas (in `"atm"`)

• `R` is the universal gas constant, equal to `0.082057("L"·"atm")/("mol"·"K")`

• `T` is the absolute temperature of the gas (in `"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).