Assume that we fill a spherical balloon from a bottle of

Chapter 3, Problem 206HP

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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.

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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

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