All books

Professional

Apps About Coach Log in Start reading

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: 1 mol1\,\mathrm{mol} contains NA=6.02×1023 N_A = 6.02 \times 10^{23}\, of them, each about 0.3 nm0.3\,\mathrm{nm} across; in a gas at ordinary conditions they are 3 nm3\,\mathrm{nm} apart, move at hundreds of meters per second and collide every 70 nm70\,\mathrm{nm} or so. At the macroscopic scale a system is described by a few state variables — pressure 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 300 K300\,\mathrm{K}: u=3×8.314×300/0.028=517 m/su = \sqrt{3 \times 8.314 \times 300/0.028} = 517\,\mathrm{m}/\mathrm{s}; hydrogen, 1930 m/s1930\,\mathrm{m}/\mathrm{s}; the heavier the slower, as 1/M1/\sqrt M. At 1 bar1\,\mathrm{bar} and 300 K300\,\mathrm{K}, n∗=P/kBT=2.4×1025 m−3n^* = P/k_BT = 2.4 \times 10^{25}\,\mathrm{m}^{-3}: 24 L24\,\mathrm{L} per mole, 2.7×1022 2.7 \times 10^{22}\, molecules in a liter. A classroom of 200 m3200\,\mathrm{m}^{3}: 8300 mol8300\,\mathrm{mol}, 240 kg240\,\mathrm{kg} of air.

Read in context →