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210.


Problem 23.35 (RHK)


The envelope and basket of a hot-air balloon have a combined mass of 249 kg, and the envelop has a capacity of . When envelope is fully inflated with the hot air it provides a lifting capacity of 272 kg (in addition to its own mass). Assuming that the surrounding air, at , has a density of , we have to find the temperature of hot air that provides the required lift.


Solution:           Click For PDF Version

Data of the problem are:

volume of the hot air balloon

combined mass of basket and envelope

total lift to achieved and

density of the surrounding air

Let the density of hot air inside the balloon that provides the required lift be

From the buoyancy principle, we have

Assuming ideal gas equation, relation between pressure, p, density, , and temperature, T, is

where M is the molar mass. It is given that the temperature of the surrounding air is and its density is . As the pressure of the surrounding air outside the balloon and that of hot air inside the balloon are the same, we have the condition