The ideal gas equation:

$\overline{){\mathbf{P}}{\mathbf{V}}{\mathbf{=}}{\mathbf{n}}{\mathbf{R}}{\mathbf{T}}}$

The density of an ideal gas:

$\overline{){\mathbf{\rho}}{\mathbf{=}}\frac{\mathbf{n}\mathbf{m}}{\mathbf{V}}}$

Weight of the hot air = m_{h}g = ρ_{h}V_{1}g

Total weight, W, of the ballon including the hot air inside:

W = m_{b}g + ρ_{h}V_{1}g

The Buoyant force on the balloon is equal to the weight of cold air displaced:

Hot air balloons float in the air because of the difference in density between cold and hot air. Consider a balloon in which the mass of the pilot basket together with the mass of the balloon fabric and other equipment is *m*_{b}. The volume of the hot air inside the balloon is *V*_{1} and the volume of the basket, fabric, and other equipment is *V*_{2}. The absolute temperature of the hot air at the bottom of the balloon is *T*_{h} (where *T*_{h} > *T*_{c}). The balloon is open at the bottom, so that the pressure inside and outside the balloon is the same. Assume that we can treat air as an ideal gas. Use *g* for the magnitude of the acceleration due to gravity. For the balloon to float, what is the minimum temperature *T*_{min} of the hot air inside in terms of the variables given?

Frequently Asked Questions

What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Buoyancy & Buoyant Force concept. You can view video lessons to learn Buoyancy & Buoyant Force. Or if you need more Buoyancy & Buoyant Force practice, you can also practice Buoyancy & Buoyant Force practice problems.