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Assume that we fill a spherical balloon from a bottle of
Chapter 3, Problem 206HP(choose chapter or problem)
Problem 206HP
Assume that we fill a spherical balloon from a bottle of helium gas. The helium gas provides work ∫ PdV that stretches the balloon material ∫ s dA and pushes back the atmosphere ∫ P0 dV. Write the incremental balance for dWhelium = dWstretch + dWatm to establish the connection between the helium pressure, the surface tension s, and P0 as a function of the radius.
Questions & Answers
QUESTION:
Problem 206HP
Assume that we fill a spherical balloon from a bottle of helium gas. The helium gas provides work ∫ PdV that stretches the balloon material ∫ s dA and pushes back the atmosphere ∫ P0 dV. Write the incremental balance for dWhelium = dWstretch + dWatm to establish the connection between the helium pressure, the surface tension s, and P0 as a function of the radius.
ANSWER:
Solution 206 HP
Step 1 of 3
We have to write the incremental balance for to establish the connection between the helium pressure, the surface tension , and as a function of the radius.
The work done by the helium gas in stretching the balloon material and pushing back the atmosphere is .
where,
helium pressure in Pa
change in the volume of
the balloon in m3