- #1
Kiarash
- 9
- 0
Temperature of a system is defined as
$$\left( \frac{\partial \ln(\Omega)}{ \partial E} \right)_{N, X_i} = \frac{1}{kT}$$Where Ω is the number of all accessible states (ways) for the system. Ω can only take discrete values. What does this mean from a mathematical perspective? Many people say we have 10^23 particles so Ω is almost continuous function of energy. Why is 10^23 a nice number but 1000 is not? When can one be sure they can differentiate ln(Omega)?
If you agree with me, do you know an alternative accurate definition for temperature?
$$\left( \frac{\partial \ln(\Omega)}{ \partial E} \right)_{N, X_i} = \frac{1}{kT}$$Where Ω is the number of all accessible states (ways) for the system. Ω can only take discrete values. What does this mean from a mathematical perspective? Many people say we have 10^23 particles so Ω is almost continuous function of energy. Why is 10^23 a nice number but 1000 is not? When can one be sure they can differentiate ln(Omega)?
If you agree with me, do you know an alternative accurate definition for temperature?