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# Thermal physics summary

## Summary of temperature, heat and thermodynamics

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.

## Summary of ideal gases

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.