Balloon Vacuum: Pressure Calculation w/ R0, σ

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Homework Statement


Balloon in vacuum, radius R0 = 5,0 cm, surface tension σ = 25 N/m.

a/ the pressure in the balloon p in,0 by radius R0………. pin,0 = ?

b/ relation to the pressure inside the balloon pin, depending on its radius R…?

c/relation to the pressure inside the balloon pin , depending on the pressure outside the balloon pout and on its radius R, surface tension is σ…….?

Homework Equations


a/ pin,0=4σ/R0 = 4.25/0,05 = 2kPa

b/ pin = 4σ/R

c/ pin = pout + 4σ/R

The Attempt at a Solution

 
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in B/ I have to use pressure p in 0...

p in = 4σ/R ...R = R0 + ΔR = R0 + ( R-R0)...p in = 4σ/R0 + ( R-R0)
 
so:?

p in = p in 0 + 4σ/ ( R- R0)
 
That looks wrong, no matter how I interpret the notation, and I don't see how you got it. In particular, it is undefined for the easiest case of R=R0.

Why do you want to change a correct answer?
 
Because I have to find dependence p in on p in 0 : Find the equation for the pressure p in inside the balloon, depending on the radius R, where
at radius R 0 is pressure p in 0
 
That's not what you write in post 1.
charlie05 said:
b/ relation to the pressure inside the balloon pin, depending on its radius R…?
 
Yes, it's true, I did not read the assignment to the end :-( I am sorrry...
 
charlie05 said:
Because I have to find dependence p in on p in 0 : Find the equation for the pressure p in inside the balloon, depending on the radius R, where
at radius R 0 is pressure p in 0
Your notation is hard to interpret, but I think you are saying:
With zero external pressure, the radius is R0 and the internal pressure is pin0.
With some unknown external pressure the radius is R; what is the internal pressure, pin, now?

If that is right, write out the equation for each of the two circumstances. Please use subscripts, as I have, to make the notation clearer. Use the X2 button above the text entry box.
 
Last edited:
b/ Find the equation for the pressure p in inside the balloon, depending on the radius R, where
at radius R 0 is pressure p in 0
 
charlie05 said:
b/ Find the equation for the pressure p in inside the balloon, depending on the radius R, where
at radius R 0 is pressure p in 0
Yes, that agrees with my interpretation. So what two equations can you write, one for the zero external pressure case and one for the general case?
 
in vacuum : ...pin = 4σ/R...for R0 ...pin0 = 4σ/R0
p in = 4σ/R ...R = R0 + ΔR = R0 + ( R-R0)...p in = 4σ/ (R0 + ( R-R0))
- But here now I can not express pin0

for the general case: pin = pout + 4σ/R
 
charlie05 said:
in vacuum : ...pin = 4σ/R...for R0 ...pin0 = 4σ/R0
p in = 4σ/R ...R = R0 + ΔR = R0 + ( R-R0)...p in = 4σ/ (R0 + ( R-R0))
- But here now I can not express pin0

for the general case: pin = pout + 4σ/R
It's all the same balloon and contents. What does not vary as the external pressure changes?
 
the amount of air in the balloon ?
 
pin0V0=pinV
pin = pin0*V0 / V = pin0 * (V0 / V ) = pin0 * (R03 / R3 ) ...?
 
super..thanks very much :-)
 
oh yes...pin = pout + 4σ/R...?
 
once again thank you very much for your help...
 

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