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Thermal physics summary

Thermal equilibrium: same temperature between different systems.

Thermodynamic temperature (Kelvin) : $$T (\text{K})=T(^{\circ}\text{C})+273.15$$.

  • Absolute zero : $$T=0 \text{ K}$$
  • Triple point of water: $$T=273.16 \text{ K}$$

Heat capacity: $$C=\frac{Q}{\Delta T}$$.

  • Specific heat capacity: $$c=\frac{Q}{m\Delta T}$$

Latent heat ($$L$$): heat exchanged with $$T=\text{constant}$$ (e.g. phase transition).

  • Specific latent heat $$\ell=Q/m$$

First law of thermodynamics ($$U=$$internal energy):

$$$\Delta U=Q+W$$$
  • Positive/Negative quantities = gained/lost by the system.

Work done by the system if $$p=\text{constant}$$ : $$W=p\Delta V$$

Types of thermodynamic processes:

  • Isochoric: $$V=\text{constant}$$
  • Isobaric : $$P=\text{constant}$$
  • Isothermal : $$T=\text{constant}$$
  • Adiabatic : $$Q=0$$

$$p=$$ pressure; $$m=$$ mass of the system; $$V=$$ Volume.

Ideal gas equation:

$$$pV=nRT=NkT$$$
  • $$N=nN_{\text{A}}$$
  • $$R=kN_{\text{A}}$$

For Ideal gas : $$U=\frac{3}{2}NkT $$

  • Mean kinetic energy of a gas particle: $$\frac{1}{2}m\langle v^{2}\rangle=\frac{3}{2}kT$$

Root mean square speed of a gas particle:

$$$v_{\text{rms}}=\sqrt{\langle v^{2}\rangle}=\sqrt{\frac{3kT}{m}}$$$

$$p=$$ pressure; $$V=$$ volume; $$n=$$ number of moles; $$m=$$ mass of a particles of gas; $$N=$$ number of particles; $$R=$$ molar gas constant $$(R=8.314\text{ m}^{2}\text{ kg}\text{ s}^{-2}\text{ K}^{-1})$$; $$k=$$ Boltzmann constant $$(k=1.38\times10^{-23}\text{m}^{2}\text{kg s}^{-2}\text{ K}^{-1})$$; $$N_{\text{A}}$$ Avogadro constant $$(N_{A}=6.02\times10^{23})$$; $$T=$$ thermodynamic temperature; $$U=$$ internal energy.