Volume of a solid at absolute zero

In summary, the conversation discusses the accuracy needed to calculate the average distance between atoms in a solid at room temperature and how it relates to the vibrational frequency. The coefficient of linear thermal expansion and its relationship to shrinkage is also mentioned. The conversation also delves into the definition of "distance between atoms" and how it changes with temperature. Finally, the properties of Ice Ih at different temperatures are briefly discussed.
  • #1
em3ry
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Volume of a solid at absolute zero
How much does a typical solid shrink when cooled from room temperature to absolute zero. I can't solve this myself because the coefficient of linear thermal expansion varies with temperature
 
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  • #2
How accurate do you need to be?
 
  • #3
accurate enough that I can calculate the average distance between atoms in a solid at room temperature so I can calculate the vibrational frequency when given the velocity of the atoms. Now I know there might be better ways to calculate the vibrational frequency but I want to do it this way first.
 
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  • #4
That doesn't really answer the question. You could do the calculation with the room temperature spacing. If you say "that's not accurate enough", we're right back to "How accurate do you need to be?"

In any event, the coefficient of thermal expansion is often linear in T. In that case, the shrinkage is half of what it would be by using the room temperature coefficient.
 
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  • #5
The room temperature spacing (minus the atomic radius) is exactly what I am trying to calculate. The easiest way to do that is to determine how much solids shrink. The spacing should be zero absolute zero

If the coefficient is linear than I should be able to figure this out
 
  • #6
em3ry said:
The spacing should be zero absolute zero
What ?
 
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  • #7
The distance between atoms. Not the distance between atom centers.
 
  • #8
em3ry said:
The distance between atoms. Not the distance between atom centers.
How do you define "the distance between atoms"? Atoms are not billiard balls. They don't have a well defined "edge".
 
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  • #10
I have already calculated the radii for all elements for multiple allotropes.
 
  • #11
em3ry said:
The distance between atoms. Not the distance between atom centers.
So are you saying that at absolute zero, you model the atoms like billiard balls, all still, and packed together, without any gaps at the surface contacts. You hypothesise that as the material is heated, the average KE increases, the balls move about more but remain bonded, and the average gap between the balls must increase, because billiard balls are incompressible?
 
  • #12
Ice Ih has the property of having a density maximum at 62 K. Yes, it shrinks on cooling above absolute zero.
 

1. What is the definition of "volume of a solid at absolute zero"?

The volume of a solid at absolute zero is the theoretical minimum volume that a solid can occupy when it is at the lowest possible temperature, which is 0 Kelvin or -273.15 degrees Celsius.

2. How is the volume of a solid affected by temperature?

As temperature increases, the volume of a solid also increases due to thermal expansion. On the other hand, as temperature decreases, the volume of a solid decreases until it reaches its minimum at absolute zero.

3. Is the volume of a solid at absolute zero equal to zero?

No, the volume of a solid at absolute zero is not equal to zero. While it is at its minimum, it is not completely compressed to a point of having zero volume. It still has a finite volume, but it is the smallest possible volume for that particular solid.

4. Why is the volume of a solid at absolute zero important?

The volume of a solid at absolute zero is important because it is a fundamental concept in thermodynamics and helps us understand the behavior of matter at extreme temperatures. It also has practical applications in fields such as material science and engineering.

5. Can the volume of a solid at absolute zero be measured?

No, the volume of a solid at absolute zero cannot be measured directly since it is a theoretical concept. However, it can be estimated through mathematical models and experiments at very low temperatures close to absolute zero.

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