Professional Guide to Calculating Hot Air Balloon Temperature

How can we determine the temperature of the hot air required to lift a hot air balloon off the ground?

Consider a hot-air balloon with a combined mass of 315 kg and containing 845 m^3 of hot air. The air outside the balloon has a temperature of 20.2°C and a pressure of 0.916×10^5 Pa. The pressure of the hot air inside the balloon is the same as the air outside. What is the temperature (°C) of the hot air needed to lift the balloon?

Answer:

To find the temperature of the hot air required to lift the balloon, we can use Archimedes' principle and the ideal gas law.

First, we need to find the density of the air outside the balloon by using the ideal gas law. The density of the air outside is approximately 1.124 kg/m^3.

Next, we can use Archimedes' principle to find the density required for the air inside the balloon. The net force on the air inside the balloon is equal to the weight of the air it displaces, which is equal to the mass of the air times the acceleration due to gravity. Setting this net force equal to the buoyant force gives us an equation to solve for the density inside the balloon.

Finally, we can use the ideal gas law again to find the temperature of the hot air inside the balloon, which is approximately 252.5 °C.