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

Answer 1

Caleb Adams

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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Answer 2

Noah Aldrich

The density of gas in a hot air balloon decreases as the gas is heated because heating the gas causes its molecules to gain kinetic energy, leading to increased movement and spreading out of the molecules. This results in a decrease in the number of gas molecules per unit volume, which lowers the density of the gas.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.