You will need to design a spherical hot-air balloon neutrally buoyant in air at

Question

You will need to design a spherical hot-air balloon neutrally buoyant in air at an ambient temperature of 273K with a load of 500 kg (that includes all connective gear and hardware). Derive an equation that relates two design parameters: the radius of the balloon and the temperature of the air inside. Make a graph showing the temperature of the hot air versus the radius in the range from 1 meter to 10 meters. Describe what the physical interpretation of the graph is (how the temperature varies with increasing radius). What combination(s) of size and temperature would be practical?

For Your Information: The density of the air at T=273K and standard atmospheric pressure is 1.3 kg/m3.

According to the ideal gas law, the density of the air is inversely proportional to the temperature on the Kelvin scale .

I know that _hot/ _cold = T_cold/T_hot, there is an inverse relationship.

Any help would be great. Thank you in advance

Explanation / Answer

From Ideal Gas Law:

PV = nRT

As, Volume of spherical ballon is directly propotional to the Temperature of the air inside at constant Preasure

Volume of spherical ballon is 4/3 * pi *r3 , So if radius in increasing, the temperature will be increased at const preasure

Graph between V and T will be linear in nature

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