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  ...