# What is temperature?

by rogerk8
Tags: temperature
 P: 183 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
 Thanks P: 1,948 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
Mentor
P: 15,167
 Quote by rogerk8 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.

P: 183
What is temperature?

 Quote by D H 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.
 P: 887 Temperature tells you which direction heat will travel. For positive temperatures, heat will travel from a higher temperature to a lower temperature. The end result is an increase in entropy. This will continue until temperatures are equal, at which point the entropy is at a maximum.

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