Ideal Gas law and a hot air balloon problem

[wilsbran]

My physics problem is as following,
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?
we are told to use a radius of 15m

Equations needed
density = m/V
ideal gas law PV=nRT
Pressure = Force over area.

This is what i Have so far:

Fnet = Fbuoyant - Fgravity
because the balloon is assumed to be in equilibrium Fnet = zero
0= density*V*g -(mass of air+mass of payload)*g
Its here that i start to get confused. I think that the density is the density of the air alone because it is the buoyant force of the heated air pushing up on the balloon so to speak.
I know that there is a relation to the gas law and from that the temperature of the balloon can be calculated...but i am stuck at this:
P= density*R*T

any suggestions/help?

 

[kuruman]

You can easily find an expression F_buoyant using Archimedes's principle. What is F_gravity? It's the weight of the unfilled balloon plus the weight of the hot air in it. If you are going to use the ideal gas law (which you should) you need to consider the pressure of the hot gas.

 

[wilsbran]

i have used the expression for the buoyant force

density*V*g = (mass of air+mass of payload)*g -------> eqn (1)

where density*V*g is the the buoyant force

i am having trouble relating it to the gas law. I know that

density = m/V

so PV=nRT can be seen as

P = density*R*T / Molar Mass

but from the force equation (eqn (1) above) i have I'm not sure how to proceed as i do not know the mass of the air.

 

[kuruman]

The mass of the air is m_air=Nm, where N = number of molecules and m = mass of one molecule. Use the ideal gas law in the form pV = NkT to replace N in the mass expressions for the gas inside and outside the balloon.