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Chapter 1: Q.1.15 (page 8)

Estimate the average temperature of the air inside a hot-air balloon (see Figure 1.1). Assume that the total mass of the unfilled balloon and payload is 500 kg. What is the mass of the air inside the balloon?

Short Answer

Expert verified

The mass of air inside the balloon isma=(500)ToTi

Step by step solution

01

Given information

mass of unfilled balloons and payload is mb=500kg

The temperature of air inside the balloon is Ti

The temperature outside the air balloon is To

molar mass of dry air is Ma

mass of air inside the balloon is ma

density of air is蚁a

02

Explanation

The buoyant force of the air and the gravitational pull on the balloon are in equilibrium:

FB,a=Fg,a

From which follows:

蚁agV=mbg

Rewriting as an expression for volume:

V=mb蚁a

Using the ideal gas law in terms of density:

V=mbRToMaP

Rewriting the ideal gas law, in this case in terms of the amount of moles of air inside the balloon:

n=PVRTi=mbMaToTi

Finally, the mass of the air inside is given by the relation:

ma=mbToTi

Plugging the value of mass of balloon in the above equation, we get,

ma=(500)ToTi

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