# Kinetic energy of a balloon

How do I quantify how much kinetic energy would be released from popping a balloon?

I believe that any additional kinetic energy that results from the balloon will come from it being pressurized, but how is that calculated?

There are two components to the total energy in the balloon:

1) The P*V work done on the air (or whatever fluid you've filled it with) and

2) the stress*strain work done on the rubber as the balloon expands. The latter is tricky to calculate (due to rubber's nonlinearity, large-strain modeling of the membrane, etc.)

If one starts from an uninflated balloon, all the work is done by forcing the fluid into the balloon. So you might measure the pressure and flow rate (dv/dt) -- ideally sampled simultaneously) -- from uninflated to the bursting point, and numerically integrate P * delta_Volume, from (negligible initial volume) up to the bursting volume (and pressure) of the balloon.

My guess is that consumer balloons have somewhat uneven wall thicknesses, so expect a fairly wide range of results.

• Interesting. If I assume, for the sake of simple calculations, that the balloon never expands (and was always at its fully inflated size), I could simply use the pressure x volume to acquire an answer in Joules? Jul 8 '19 at 1:59
• Simply multiplying the (final) pressure and (final) volume will give you an incorrect answer for 2 reasons: first, that would completely ignore the stress * strain work, but it would also get the PV work wrong, because the pressure is not constant! See ideal gas law. So you've gotta integrate P * dv from P0 up to Pfinal to get the fluid portion of the energy correct. Jul 8 '19 at 11:19
• I don't see why any integration is needed. Pressure is a state function and so only the final value should matter. Perhaps I should restate how I am seeing the problem. Let's pretend that the baloon is a rigid, fixed wall sphere that does not appreciably expand. I think that the energy released from this sphere being popped should be the final pressure x volume of the container. Jul 8 '19 at 16:47
• Re the need for integration, please see a basic text on thermodynamics, specifically how to calculate the enthalpy of a control volume of gas. Your stated problem is about popping a balloon; ballons only pop if they can stretch (variable volume.) A rigid no-longer-remotely-like-a-balloon simply wouldn't pop! Would you kindly stick to your original question (elastic balloon popping) -- or else ask your new variation as separate questions the multiple changes -- in comments yet -- is not good stack exchange behavior, IMHO! Jul 8 '19 at 23:34