# Ideal gas law problem?

1. Feb 2, 2014

### annas425

A spherical helium balloon 11 m in diameter is at ambient temperature and pressure, 15 degrees Celsius and 100 kPa. How much helium does it contain? It can list a total mass of balanced atmospheric air. How much mass of the balloon fabric & cage can then be lifted?

Here is my work but I'm unsure if it's correct. If someone could let me know I would really appreciate it. I also don't know how to answer the second part of the problem at all. Thanks in advance!

r = 5.5 m
T = 15°C = 288.15 K
P = 100 kPa = 100 kN/m
R = .287 kN m/kg K

m = PV/RT = 842.69 kg Helium

2. Feb 2, 2014

### haruspex

You seem to have hybridised two formulae:
PV = mRspecT
PV = nRT
where m is mass, n is number of moles, and Rspec is a constant specific to the gas.

3. Feb 2, 2014

### Staff: Mentor

What did you get for the volume of the balloon?

Does it really make sense to you that a balloon of this volume can hold close to a metric ton of helium at atmospheric pressure?

chet