Negative absolute temperature exists!
Believe it or not, negative Kelvin exists, and it's not cold, it's really hot! It is an unusual way to introduce students to the field of statistical mechanics (aka statistical physics), but I feel it is a highly engaging approach to introducing this challenging topic in physical chemistry and physics. I love teaching this topic, and I hope you enjoy it too!
0:00 – Intro and overview
0:07 – Can temperature be negative?
0:29 – Why we usually say “no” — and when that fails
1:05 – Defining temperature from thermodynamics (entropy and energy)
1:36 – Entropy as a function of internal energy
2:33 – Why most systems have increasing entropy with energy
3:01 – When could entropy decrease as energy increases?
3:34 – The key idea: negative slope means negative temperature
3:46 – Spin systems in a magnetic field (NMR connection)
4:54 – Two-level system: aligned vs. anti-aligned spins
6:21 – Setting up energy levels for aligned and anti-aligned states
6:27 – Many spins in a magnetic field — absolute zero case
7:19 – Heating the system and thermal fluctuations
8:30 – How random “kicks” change spin alignment
9:38 – What happens as temperature approaches infinity
10:31 – Entropy and maximum disorder (half up, half down)
11:43 – Counting microstates and understanding entropy mathematically
13:09 – When entropy decreases as energy increases
14:31 – Creating a population inversion by flipping the field
15:08 – What “hotter than infinity” really means
16:31 – Understanding negative temperature through DS/DU reasoning
17:45 – Simulating magnetic reversal with an electromagnet
19:17 – Observing energy, entropy, and temperature in the simulation
22:07 – Cooling from negative to positive temperature
23:11 – The full relaxation process explained
23:47 – Historical experiment: Purcell and Pound, Harvard 1950
25:00 – What their results showed and why it matters
25:27 – Heat flow, the Second Law, and the paradox resolved
26:28 – Why negative temperatures are hotter than any positive one
26:54 – Final reflections: what this teaches about temperature itself