pressure variations

[Uno Qualunque]

Hi

inside a sphere buried within a elastic ideal medium at pressure P1 I
create a variation of pressure of dP. What variation dPx I would measure
if the sphere was buried in a medium at pressure P2 using the same
energy? Is it possible to solve this problem?

Sorry I'm not a physicist

Thank you

Jen

[Richard Livingston]

Jen,

There is not enough information to give a complete answer, or perhaps
I don't understand exactly what you are describing. If by "elastic ideal
medium" you mean an ideal gas, and by "a sphere buried within" you
mean a bubble (i.e. no shell or balloon skin that would affect the size
and stiffness of the sphere) then the problem is no different than an
ideal gas in a cylinder being held a constant pressure. However in
that case the pressure would remain constant as the volume of the
bubble increases. That is, you would not be able to increase the
pressure.

If instead you mean a rapid ("instantaneous") increase in pressure
inside the sphere, then the work would be dW = VdP, where V is the
initial volume of the bubble. But then the bubble would start to
expand until its pressure returned to the ambient.

If by "elastic ideal medium" you mean a solid, then you must know
the stiffness of the solid as the spherical hole will expand somewhat
as the pressure is increased. That expansion will take some work
(energy).

I'm not sure if any of that is a useful answer to you. Depending on
exactly what your problem is this can be quite complicated.

Rich L.