Physics · Glossary

What is Microscopic and macroscopic scales?

Definition 20.1 University Physics — Year 1 · Chapter 20 — Kinetic Theory and the Perfect Gas

At the microscopic scale matter is made of molecules: 1mol1\,\mathrm{mol} contains NA=6.02×1023N_A = 6.02 \times 10^{23}\, of them, each about 0.3nm0.3\,\mathrm{nm} across; in a gas at ordinary conditions they are 3nm3\,\mathrm{nm} apart, move at hundreds of meters per second and collide every 70nm70\,\mathrm{nm} or so. At the macroscopic scale a system is described by a few state variablespressure PP, volume VV, temperature TT, amount of substance nn — that are averages over enormous numbers of molecules. A variable is extensive if it doubles when the system is doubled (VV, nn, mass, energy), intensive if it does not (PP, TT, density).

Examples

Example 20.8 (Numbers for air)

Nitrogen at 300K300\,\mathrm{K}: u=3×8.314×300/0.028=517m/su = \sqrt{3 \times 8.314 \times 300/0.028} = 517\,\mathrm{m}/\mathrm{s}; hydrogen, 1930m/s1930\,\mathrm{m}/\mathrm{s}; the heavier the slower, as 1/M1/\sqrt M. At 1bar1\,\mathrm{bar} and 300K300\,\mathrm{K}, n=P/kBT=2.4×1025m3n^* = P/k_BT = 2.4 \times 10^{25}\,\mathrm{m}^{-3}: 24L24\,\mathrm{L} per mole, 2.7×10222.7 \times 10^{22}\, molecules in a liter. A classroom of 200m3200\,\mathrm{m}^{3}: 8300mol8300\,\mathrm{mol}, 240kg240\,\mathrm{kg} of air.

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