Calculate Sphere Volume: P, T, Radius

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Homework Help Overview

The discussion revolves around calculating the volume of air in a sphere, specifically in the context of a rubber balloon, given parameters such as pressure (P), temperature (T), and radius. Participants explore how these factors interact in determining the volume of air within the balloon.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants discuss the relationship between the radius of the balloon and the volume of air it contains, questioning how the ideal gas law applies in this context. There are attempts to clarify whether the balloon's volume can be directly calculated from the radius alone.

Discussion Status

The conversation is active, with participants offering different perspectives on the relationship between pressure, temperature, and radius. Some suggest using the ideal gas law, while others emphasize the geometric volume of the sphere. There is an ongoing exploration of how these variables are interconnected.

Contextual Notes

Participants note that the balloon is not rigid and can stretch, which adds complexity to the problem. There is also a mention of the real gas law in relation to the ideal gas law, indicating that assumptions about the gas behavior may be under discussion.

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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