Calculating Temperature Needed for Hot Air Balloon Lift

[scarlson1193]

Homework Statement

A man wants to go on a hot air balloon trip, and wants to build a balloon with a capacity of 10,000 m^3. The envelope and the balloon have a combined mass of 250 kg. His luggage would be 800 kg. Assume that the ambient air is at a temperature of 20 degrees Celsius. What must the temperature of the air inside the balloon be to provide the required lift?

Homework Equations

The ideal gas law: P = ρRT

Archimedes' Principle: density of object/density of fluid = weight/weight-apparent immersed weight

The Attempt at a Solution

My lab group is not entirely sure where to start with this. We feel that these two formulas will be useful simply because when we examine other similar problems, they come up, but we aren't sure where to start or how to get our information into these formulas so they will work properly. Can we get some help on where to even begin with this problem?

 

[ehild]

You can take the volume of the balloon constant and also the pressure of air in the balloon equal to the atmospheric pressure.
Find the expression for ρ(T) knowing that the density of air at 20°C is 1.2041 kg/m³,
(http://en.wikipedia.org/wiki/Density_of_air)

and apply Archimedes' Principle. The total weight of the balloon and load and the air in it is equal to the volume of the balloon multiplied with the density of the cold air.

ehild