Hot Air Balloon Density Calculation

What happens to the air density inside a hot air balloon when the temperature is increased? Explanation: When the temperature inside a hot air balloon is increased, the air density decreases. This is due to the inverse relationship between density and temperature according to the ideal gas law.

Relationship between Air Density and Temperature

Density and temperature of a gas are inversely related. As the temperature of a gas increases, its density decreases, and vice versa. This phenomenon can be explained by the ideal gas law, which states that the pressure of a gas is directly proportional to its temperature and inversely proportional to its volume.

Impact of Temperature Increase on Hot Air Balloon Density

When the burner of a hot air balloon is lit and the air inside the balloon is heated, the temperature of the air increases. As a result, the air molecules gain kinetic energy and move faster, causing them to spread out and occupy a larger volume. This increase in volume leads to a decrease in air density inside the balloon.

Calculation Example

Assuming an initial air temperature of 20°C (293K) and density of 1 kg/m^3, if the temperature inside the balloon is raised to 30°C (303K), the new air density can be calculated using the ideal gas law formula:

p2 = p1 * (T1 / T2)

where:

p1 = initial density = 1 kg/m^3

T1 = initial temperature = 293K

T2 = final temperature = 303K

By substituting the values:

p2 = 1 * (293 / 303)

p2 = 0.967 kg/m^3

Therefore, the new air density inside the hot air balloon after heating to 30°C is approximately 0.967 kg/m^3, which is lower than the initial density of 1 kg/m^3.
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