- #1

Suraj M

Gold Member

- 599

- 39

^{-1}K

^{-1}) so different from the predicted value of 3R≈25??

You are using an out of date browser. It may not display this or other websites correctly.

You should upgrade or use an alternative browser.

You should upgrade or use an alternative browser.

- Thread starter Suraj M
- Start date

- #1

Suraj M

Gold Member

- 599

- 39

- #2

DrClaude

Mentor

- 7,758

- 4,268

Is the specific heat independent of temperature?

- #3

Suraj M

Gold Member

- 599

- 39

strictly speaking it does depend on temperature, but is often ignored due to the insignificance of the deviation.Is the specific heat independent of temperature?

- #4

DrClaude

Mentor

- 7,758

- 4,268

The deviation is far from insignificant, as at low temperature the heat capacity has to go to zero. And what can be called "low" temperature is very relative. At room temperature, carbon (be it diamond or graphite) is far from the asymptotic limit given by the Dulong-Petit law.strictly speaking it does depend on temperature, but is often ignored due to the insignificance of the deviation.

- #5

Suraj M

Gold Member

- 599

- 39

Everywhere they say, 'due to their high energy vibrational modes not being populated at room temperature' ?

- #6

DrClaude

Mentor

- 7,758

- 4,268

The Dulong-Petit law works if you can apply the equipartition theorem, that is if all quadratic degrees of freedom have an average energy ##\langle E \rangle = k_B T / 2##. Since vibration is quantized, this can only be the case for the vibrational modes if there is enough energy to significantly populate excited states. Some solids have such a high threshold that you need to go very high temperatures before you have sufficient excitation and can neglect the discrete (quantized) aspect of vibrational energy.

Everywhere they say, 'due to their high energy vibrational modes not being populated at room temperature' ?

- #7

Suraj M

Gold Member

- 599

- 39

- #8

DrClaude

Mentor

- 7,758

- 4,268

Not that I know. You can do it empirically, by finding a function that fits the observed heat capacity, or computationally.

- #9

Suraj M

Gold Member

- 599

- 39

ohh! okay, thank you for your help.

- #10

- 3,896

- 518

You can think in terms of room temperature not being a "high temperature" for diamond. This is suggested for example by the value of Debye temperature, which is over 2000 K. For metals the same value is just a few hundred K.

Share: