Expansion and Temperature

In summary, for particles with mass m, the number density n is proportional to T^{3/2}exp[-(m-\mu)/T] for T>m, and proportional to T^{-3} for T>m. However, the relationship for T>m cannot be derived using n\propto a^{-3} due to the presence of pair production.
  • #1
Arman777
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For ##m>T## we can write
$$n\propto T^{3/2}\exp[{-(m-\mu)/T}].\tag{2}$$

For ##T>m## we can write ##n\propto T^{3}## where ##n## is number density of particles with mass m. We can derive this relationship by using ##n\propto a^{-3}## and we also know that ##a\propto T^{-1}##.

Is there a similar derivation for the first equation by using ##n\propto a^{-3}##
 
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  • #2
Can you elaborate?
 
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  • #3
I edited my post
 
  • #4
I'm guessing the question is about particle densities in the early universe? Then a is the scale factor.
Arman777 said:
For ##T>m## we can write ##n\propto T^{-3}## where ##n## is number density of particles with mass m. We can derive this relationship by using ##n\propto a^{-3}## and we also know that ##a\propto T^{-1}##.
Shouldn't this be ##n\propto T^{3}##? ##n\propto a^{-3}## assumes no particles can be produced or destroyed. Is that really an assumption you want to make - and if you do so, why don't you make it for m>T?
 
  • #5
mfb said:
I'm guessing the question is about particle densities in the early universe? Then a is the scale factor.Shouldn't this be ##n\propto T^{3}##? ##n\propto a^{-3}## assumes no particles can be produced or destroyed. Is that really an assumption you want to make - and if you do so, why don't you make it for m>T?
If ##n\propto a^{-3}## assumes no pair production then we cannot say that at ##m>T##, since at that time there are pair-production, So we cannot derive it by using ##n\propto a^{-3}##.
 

1. How does temperature affect the expansion of matter?

Temperature directly affects the expansion of matter. As the temperature increases, the particles in matter gain more energy and move faster, causing them to take up more space and expand. Conversely, as the temperature decreases, the particles lose energy and move slower, causing the matter to contract and take up less space.

2. What is thermal expansion and how does it work?

Thermal expansion is the process by which matter, such as solids, liquids, and gases, expands or contracts in response to changes in temperature. This occurs because when matter is heated, its particles gain energy and move further apart, resulting in an increase in volume. The opposite happens when matter is cooled, and its particles lose energy, causing them to move closer together and resulting in a decrease in volume.

3. What is the coefficient of thermal expansion?

The coefficient of thermal expansion is a measure of how much a material will expand or contract in response to a change in temperature. It is represented by the symbol α and is expressed in units of length per degree Celsius (or Fahrenheit). Different materials have different coefficients of thermal expansion due to variations in their molecular structures.

4. How does the expansion of matter affect everyday objects?

The expansion of matter has numerous practical applications in everyday objects. For example, it is used in thermometers, which work by measuring the expansion of a liquid in a sealed tube in response to changes in temperature. It is also used in the construction of bridges and buildings, where materials are chosen based on their coefficient of thermal expansion to prevent damage from temperature changes.

5. Can materials expand and contract differently in different directions?

Yes, materials can expand and contract differently in different directions. This is known as anisotropic expansion. It occurs because the molecular structure of a material is not uniform in all directions, causing it to expand or contract at different rates. This can be seen in materials such as wood, which expands more in the direction of its grain than across it.

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