Does Thermal Expansion Affect the Enclosed Volume or the Shell Material Volume?

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Discussion Overview

The discussion revolves around the effects of thermal expansion on a spherical shell, specifically whether the volume change described by the equation V(T)=V(0)(1+yT) refers to the volume enclosed by the shell or the volume of the shell material itself. Participants explore the implications of thermal expansion on both the shell and the enclosed volume.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • One participant questions whether the volume change refers to the volume enclosed by the shell or the volume of the shell material.
  • Another participant asserts that both a spherical shell and a solid sphere of the same diameter and material will expand to the same size.
  • It is proposed that all volumes, whether of the shell material or the enclosed volume, expand by the same fraction when heated.
  • A further inquiry is made regarding the specific change in radii of the shell and the cavity upon heating, suggesting that both should increase by 'aT', where 'a' is the linear coefficient of thermal expansion.
  • A participant confirms that, assuming isotropic material properties, all linear dimensions will expand by the same fraction.

Areas of Agreement / Disagreement

Participants generally agree that both the shell material and the enclosed volume will expand, but there is some ambiguity regarding the interpretation of the volume change equation and its application to the two different volumes.

Contextual Notes

Assumptions regarding isotropy of the material and the specific conditions under which the expansion occurs are not fully detailed, leaving some aspects of the discussion unresolved.

Who May Find This Useful

This discussion may be useful for individuals interested in thermal expansion, material science, and the behavior of materials under temperature changes.

miss photon
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[SOLVED] thermal expansion

hi everybody
my question is:
a spherical shell is heated. the volume changes according to the equation V(T)=V(0)(1+yT) where y=volume coeff. of thermal expansion. does this volume refer to the volume enclosed by the shell or the volume of the material making up the shell?
 
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By the shell itself. A spherical shell and a solid one (same dia. and material) should be expanding to the same size.
 
miss photon said:
does this volume refer to the volume enclosed by the shell or the volume of the material making up the shell?
It doesn't matter. All volumes expand by the same fraction, whether you take the volume of the shell material or the volume enclosed by the shell. When the material expands, so does the volume it encloses.
 
let me put it in another way. if the shell of radius R has a spherical cavity of radius r, what will be the change in the two radii on heating? will the increase in both be 'aT' where a=linear coeff of thermal expansion?
 
miss photon said:
will the increase in both be 'aT' where a=linear coeff of thermal expansion?
Yes. Assuming the material is isotropic, all linear dimensions expand by the same fraction.
 

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