How Do You Calculate the Total Entropy of a Helium Balloon?

[Gemstone]

Me and a friend has recently fallen into a dead-end with an assignment we have, because we can't calculate the total entropy of a balloon filled with Helium.

basically, the assignment goes:
We have a balloon with 10 mol of Helium, inside a house with a temperature of 25 degrees celsius (that is, 298 kelvin). Now, we take the balloon outside to a temperature of -5 degrees clecius (268 kelvin).

Now, we're supposed to calculate the total entropy of the balloon and the environment. Anyone willing to help us out?

We've this far deducted that the pressure is 101,3 KPa (1 atmosphere)... which is by far the longest we've come.

Any help is appreiciated

 

[Agnostic]

Entropy is:

S=kLn(Ω)

Where Ω is the multiplicity of the system.

Also. ∆S=∫dQ/t

This should help get you started.

 

[Mute]

I think starting from the statistical definition of entropy would be a bit much for this problem. =P I think the formulae for ideal gases are well known enough that they can just be used right from the start.

So, since you're dealing with helium, you can indeed treat the gas in the balloon as an ideal gas.

Start with the first law: dE = -PdV + TdS

For an ideal gas, you know how pressure and volume relate: PV = nRT, and there's also a formula for the energy of an ideal monatomic gas, E = 3nRT/2. From this you can derive an equation for the entropy change given the volume change and the temperature change (recall that in these formulae temperature must be measured in Kelvins).

Hopefully that helps.

 

[Gemstone]

Thank you for your help :) We managed to solve the equation in the end