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

In summary, the conversation discusses thermal expansion and its effects on a heated spherical shell. It is determined that the volume expansion is the same regardless of whether it refers to the volume of the material or the volume enclosed by the shell. The increase in both radii of the shell and its cavity is also shown to be proportional to the linear coefficient of thermal expansion.
  • #1
miss photon
23
0
[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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  • #2
By the shell itself. A spherical shell and a solid one (same dia. and material) should be expanding to the same size.
 
  • #3
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.
 
  • #4
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?
 
  • #5
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.
 

What is thermal expansion of a shell?

Thermal expansion of a shell refers to the phenomenon in which a shell or container expands or contracts in response to changes in temperature. This is due to the fact that materials expand when heated and contract when cooled.

What causes thermal expansion of a shell?

Thermal expansion of a shell is caused by the movement and vibration of molecules within the material. When heated, these molecules have more energy and move further apart, causing the material to expand. When cooled, the molecules have less energy and move closer together, causing the material to contract.

How does thermal expansion affect the size and shape of a shell?

Thermal expansion can cause a shell to change in both size and shape. When heated, the shell will expand, causing it to become larger. This expansion can also cause the shell to change shape, becoming more curved or bulging. When cooled, the shell will contract, becoming smaller and possibly changing shape again.

What materials are most affected by thermal expansion?

All materials are affected by thermal expansion to some degree, but some materials are more susceptible than others. Generally, materials with lower thermal expansion coefficients, such as metals and glass, are less affected by temperature changes compared to materials with higher coefficients, such as plastics and rubber.

How is thermal expansion of a shell measured?

Thermal expansion of a shell can be measured using a coefficient of thermal expansion (CTE) value, which is the change in length or volume of a material per unit change in temperature. This value is typically expressed in units of mm/m°C or in./in.°F. It can also be measured using specialized instruments, such as a dilatometer, which measures the change in length or volume of a material as it is heated or cooled.

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