At a festival, spherical balloons with a radius of 160. cm are to be inflated with hot air and released. The air at the festival will have a temperature of 25°C

Question

It must be heated to 100°C to make the balloons float. 1.00kg of propane C3H8 fuel is available to be burned to heat the air. Calculate the maximum number of balloons that can be inflated with hot air.

Balloons = ______

Answer 1

There are a lot of assumptions that have to go into this problem and it depends on the class as to what those are. 1) Assume no elasticity of the balloon. 2) Assume all the air is in the balloon and the air is heated to temperature. 3) Assume all the energy supplied by the heat of combustion goes into the increased enthalpy of the balloon air (const P process)

You have to find or calculate the ΔH of combustion of propane (either look it up, or use heats of formation)

You need the volume of air at 373K in order to find the moles of air that get heated in each balloon.

V = 4/3πR³ (put R in dm or m so that you can use one of the appropriate gas constants)

n = PV/RT (P is atmospheric Pressure in the appropriate units for the gas constant)

1kg propane * heat of combustion in J/kg = (moles of air)(molar heat capacity of air)(373 - 298) * N

where N is the number of balloons. 4) Assume molar heat capacity and heat of combustion doesn't change much with T (not unreasonable given other assumptions)