# Ideal gas law/hot air balloon problem (Thermal Physics by D. Schroeder, prob 1.15)

## Homework Statement

Estimate the average temperature of the air inside a hot air balloon. Assume that the total mass of the unfilled balloon and payload is 500kg. what is the mass of the air inside the balloon?

No volume or radius is given, so I estimated V = 2800 m^3 & r = 8.75 m
estimate T = 370 Kelvin
mass of 1 molecule of air calculated to be 29.00 g/mol

## Homework Equations

PV = NkT
m{air} = # of molecules[N] * mass of 1 molecule {m}
P = mass/volume

## The Attempt at a Solution

PV = NkT ---> N = PV/kT

m{air} = (PV/kT)*m

I don't know how to find pressure w/o knowing the mass of air inside the balloon. P = F/A (surface area calculation is trivial so I'm not going to do it here). I assume F is the buoyant force?

In equilibrium, Fbuoy = Fgrav, so: Fbuoy = (m{air} + m{payload})* g

but it looks like I need m{air} to find Fbuoy. What do?

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Andrew Mason