Balloon problem, thermodynamics

[illidari]

Homework Statement

A helium balloon is used to lift a load of 110 N. The weight of the balloon's skin is 50 N, and the volume of the balloon when fully inflated is 32 m3. The temperature of the air is 0°C and the atmospheric pressure is 1 atm. The balloon is inflated with sufficient helium gas so that the net buoyant force on the balloon and its load is
30 N. Neglect changes of temperature with altitude.

(a) How many moles of helium gas are contained in the balloon?

Homework Equations

Find V from FB = mg + 30 N
PairVg = 190 N + PHeVg; V = 17.38 m3

The Attempt at a Solution

I am confused on how you get the V=17.38 from using the equation I posted. Could someone explain that part to me.

 

[gneill]

First, let me just say that the question is being a bit sloppy in using "net buoyant force" to mean the net upward force (the sum of all contributions in the vertical direction -- which includes the buoyant force due to the air displaced by helium gas).

Moving on...

The helium gas displaces an equal volume of air, thus producing lift (buoyant force). You'll need to look up the density of air and the density of helium gas (you can calculate the latter from the molar mass of helium and the molar volume of a gas at 0 degrees and 1 atmosphere pressure).

The net upward force is then (buoyant force) - weights

 

[illidari]

Didn't realize these were just stuff I had to look up...

Density air = 1.293
density helium = .1786

190/ (1.293-.1786 * 9.81) = 17.38

>.< Well an answer is an answer

Thanks!