# What is temperature?

Hi!

I wonder what temperature really is.

I have learned that temperature comes from the fact that atoms vibrate.

But in plasma physics it can be related to the actual speed of particles.

So what is temperature?

It was interesting and educational to read the new thread regarding heat capacity but I think my question requires a new thread.

By the way, is there anything wrong with the following calculation of the sun's temperature (considering the sun's radiation being isotropic):

$$I_s=\frac{P}{S_s}=\frac{P}{4\pi R_s^2}=k*T_s$$
$$I_e=\frac{P}{4\pi (AU)^2}=k*T_e$$
$$T_s=T_e*\frac{I_s}{I_e}=T_e*(\frac{AU}{R_s})^2=300*(\frac{1,5*10^{11}}{700*10^6})^2=14MK$$

I really am not sure what I have calculated but wikipedia says that the sun core temperature is some 16MK. Which is pretty close even though I was aiming at the sun's surface temperature...

Best regards, Roger

Conceptually, Temperature is a measure of the tendency to donate heat. When to objects come in contact, the one with higher temperature will donate heat to the one with lower temperature

D H
Staff Emeritus
So what is temperature?
A relation between entropy and internal energy:

$$\frac 1 T = \left(\frac {\partial S} {\partial E}\right)_{V,N}$$

By the way, is there anything wrong with the following calculation of the sun's temperature (considering the sun's radiation being isotropic):

$$I_s=\frac{P}{S_s}=\frac{P}{4\pi R_s^2}=k*T_s$$
$$I_e=\frac{P}{4\pi (AU)^2}=k*T_e$$
$$T_s=T_e*\frac{I_s}{I_e}=T_e*(\frac{AU}{R_s})^2=300*(\frac{1,5*10^{11}}{700*10^6})^2=14MK$$
You should have used the Stefan-Boltzman law. What are you using here? The units aren't even correct with your equation. The left-hand side has units of mass/time3, the right of energy (mass*length2/time2). Always check your units.

A relation between entropy and internal energy:

$$\frac 1 T = \left(\frac {\partial S} {\partial E}\right)_{V,N}$$

You should have used the Stefan-Boltzman law. What are you using here? The units aren't even correct with your equation. The left-hand side has units of mass/time3, the right of energy (mass*length2/time2). Always check your units.

Hi D H!

Let's recalculate now that I have studied the Stefan-Boltzman Law:

$$I_s=\frac{P}{S_s}=\frac{P}{4\pi R_s^2}=k*T_s^4$$
$$I_e=\frac{P}{4\pi (AU)^2}=k*T_e^4$$
$$T_s=T_e*(\frac{I_s}{I_e})^{1/4}=T_e*(\frac{AU}{R_s})^{1/2}=300*(\frac{1,5*10^{11}}{700*10^6})^{1/2}=4391K$$

Which isn't so far from 5800K.

Best regards, Roger
PS
Your entropy formula didn't say me much but now I at least have some words to google.

By the way, P stands for power which I have stolen from acoustics.

Khashishi