Hot Air Balloon Density Calculation
Relationship between Air Density and Temperature
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.