Calculate Sphere Volume: P, T, Radius

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SUMMARY

The discussion focuses on calculating the volume of air in a sphere, specifically within a rubber balloon, using the ideal gas law and geometric formulas. The volume of a sphere is determined by the formula \( \frac{4}{3}\pi r^3 \), where 'r' is the radius. The relationship between pressure (P), temperature (T), and volume (V) is established through the ideal gas law, expressed as \( \frac{P_1V_1}{T_1} = \frac{P_0V_0}{T_0} \). It is concluded that knowing P and T allows for the determination of the radius, as these variables are interdependent in the context of an ideal gas.

PREREQUISITES
  • Understanding of the ideal gas law
  • Familiarity with geometric volume calculations
  • Knowledge of real gas behavior
  • Basic algebra for manipulating equations
NEXT STEPS
  • Study the ideal gas law and its applications in real-world scenarios
  • Learn how to derive the volume of different geometric shapes
  • Explore the differences between ideal and real gas behavior
  • Investigate the effects of temperature and pressure on gas volume
USEFUL FOR

This discussion is beneficial for physicists, engineers, and anyone involved in fields requiring gas volume calculations, particularly in applications involving flexible containers like balloons.

eldon
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how do I calculate the volume of air in a sphere if I know
P, T, radius
 
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When you say in a sphere, do you mean "in a spherical container?" This is the only thing that makes sense to me. If so, then the gas will fill the container, and all you need to know is the volume of the sphere. For that, all you need to know is the radius.
 
its not a rigid tank it is rubber and can stretch
 
In that case, couldn't you just use the ideal gas law?
 
yea but how does the radius figure in
 
air volume in a balloon

How do I figure out the volume of air in a balloon if I know the radius of the balloon, the air temp, and the pressure?
 
If it's a sphere, all you need is the radius to compute the volume.
 
You know the geometric volume of the balloon. You know the pressure, the temp. Apply the real gas law formula:

P1V1/T1 = PoVo/To
 
so the volume of the sphere using 4/3*pi*r^3 would be the same as the volume of the air?
 
  • #10
how does that relate to the radius of the balloon?
 
  • #11
eldon said:
so the volume of the sphere using 4/3*pi*r^3 would be the same as the volume of the air?
Sure. Simple as that.
 
  • #12
cepheid said:
In that case, couldn't you just use the ideal gas law?

eldon said:
yea but how does the radius figure in

Maybe this is clear by now, based on other people's responses, but if you know P and T, then the radius is predetermined. It is not an independent variable. The reason is that for an ideal gas, P and T uniquely determine V, which in turn contrains the radius, since the volume is a sphere.
 

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