Thermodynamics Question...?

Question

I am having trouble with this question in my homework:

Derive an expression to estimate the work required to inflate a common balloon. List all simplifying assumptions

Thats the information it gives me

Answer 1

I've never seen this question before. However, I thought over the problem for a few mins. & my mind sprang up on the following. Maybe this might help you.

Let the gas you are inserting inside the balloon be an ideal gas. Also, assume that the rubber with which the balloon is made to be perfectly elastic, & that no energy is lost & no rise in temperature takes place inside the balloon. All other asasumptions are the same as in the Kinetic Molecular Theory of Gases.

Work done to inflate a small volume of the balloon, dW=P*dV
( pressure is constant due to the material of the balloon being perfectly elastic).
So, work done to inflate the whole balloon would be the integration of P*dV, over the limits V1 to V2, V1 & V2 are the initial & final volumes respectively..
Thus, W=P*V2 - P*V1
=PV2 - P*0 (if there is no gas initially inside the balloon, hence its initial volume is 0)
=PV2
= n*R*T2

Answer 2

Bravo, Prashant!

But, depending on the level of study that the questioner is at, the answer probably requires integration. Here's an answer that might get zero marks, if this is not what is wanted!

That air in the balloon cannot be zero to begin with.
Let it be v at the start (uninflated) with air at atmospheric pressure p.
And V at the end with pressure P.
Assume temperature does not change.

Work required is just (average pressure)*(volume change).

Work, W = (p + P)(V-v)/2

This also assumes linear increase of pressure with volume.
(Not in opposition to Boyle's Law which is for a fixed mass of gas, because you are blowing in increasing masses of air all the time.)