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

1 Answer
Nathan L.
Jun 24, 2017

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).

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