The long-form Week 1 session on the mole and PV = nRT, with the numbers actually run. Blake and Riley count the carbon atoms in a 44.5-carat diamond, take a piston cylinder from the surface down to 100 metres, sort out gauge versus absolute pressure, and show why helium outruns nitrogen by a factor of root seven at the same temperature. Along the way: two unit systems for R, the Celsius mistake that once went out in an email, and a scratchpad checklist for PHYS 251 problems.
In this episode, we cover:
1. The mole as a super-sized dozen, with worked conversions for a 44.5-carat diamond and a 138-carat ruby
2. Grams per mole versus grams per atom, and where the atomic mass unit fits in
3. PV = nRT in two unit systems (8.31 J/mol K or 0.0821 L atm/mol K), and why kelvin is non-negotiable
4. Gauge versus absolute pressure, and pressure at depth as atmospheric + rho g h — about one extra atmosphere per 10 m, not a doubling
5. A piston cylinder taken from the surface to 100 metres: finding the moles, then compressing the gas elevenfold
6. Temperature as average kinetic energy, three-halves k_B T per molecule, and three-halves nRT internal energy for a monatomic gas
7. RMS versus most probable speed, and why helium moves about 2.65 times faster than nitrogen at the same temperature
8. Everyday checks: tyre pressure on the highway, a warm bike pump, frost on a spray can, and the combined-gas-law layout that catches mistakes
Chapters:
00:00 Intro
03:17 Compounds, aluminum oxide, and keeping the counting chain clean
09:46 Depth rules of thumb: atmospheres under water
12:57 Conduction, convection, radiation — heat in plain pictures
19:31 Choosing R, SI defaults, and plugging in without panic
26:10 Flexible balloon vs piston: same law, different shell
30:55 Heat a clamped piston: pressure rises at fixed volume
34:12 Elastic collisions and what “ideal” really buys you
37:27 Tanks in hot cars: n fixed, T up, P up
40:46 Grams to fractions of a mole, and unit-system duels
47:19 Same answer in SI: cross-checking the algebra
49:23 Lightning round and takeaway
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