Thermal Physics Notes

Physical Constants: Includes values for k, N, R, h, c, G, e, me, and mp with their units. $k = 1.381 \times 10^{-23} J/K = 8.617 \times 10^{-5} eV/K$ , $N = 6.022 \times 10^{23}$ , $R = 8.315 J/mol.K$ , $h = 6.626 \times 10^{-34} J.s = 4.136 \times 10^{-15} eV.s$ , $c = 2.998 \times 10^8 m/s$ , $G = 6.673 \times 10^{-11} N\cdot m^2/kg^2$ , $e = 1.602 \times 10^{-19} C$ , $me = 9.109 \times 10^{-31} kg$ , $mp= 1.673 \times 10^{-27} kg$ .
Unit Conversions: Lists conversions for atm, bar, N/m², lb/in², mm Hg, temperature scales (°C to K and °F to °C), °R to K, cal to J, Btu to J, eV to J, and u to kg. For example, $1 atm = 1.013 bar = 1.013 \times 10^5 N/m^2 = 14.7 lb/in^2=760 mm Hg$ .
Temperature Definitions: Discusses operational (thermometer) vs. theoretical (energy exchange) definitions of temperature.
Thermal Equilibrium: Explains the concept, relaxation time, and introduces energy, volume, and particles as exchanged quantities for thermal, mechanical, and diffusive equilibria, respectively.
Ideal Gas Law: States the law in the forms $PV = nRT$ and $PV = NkT$ , defining each variable. Discusses the empirical value of R and Boltzmann's constant k. $nR = Nk$ .
Ideal Gas Model: Pressure is related to the average kinetic energy of molecules: $P = \frac{N}{V}m\overline{vx^2}$ . Equipartition of Energy: Kinetic energy relationship to temperature: $\frac{1}{2}m\overline{vx^2} = \frac{1}{2}kT$ . RMS speed: $v_{rms} = \sqrt{\frac{3kT}{m}}$ .
Equipartition Theorem: Each quadratic degree of freedom has an average energy of $\frac{1}{2}kT$ . Total thermal energy is $U_{thermal} = N f \frac{1}{2} kT$ .
Heat and Work: Defines heat as spontaneous energy flow caused by temperature differences and work as other energy transfers. First law of thermodynamics: $\Delta U = Q + W$ .
Compression Work: $W = -\int P(V) dV$ (quasistatic compression).
Isothermal Compression: $W = NkT \ln(\frac{Vf}{Vi})$ and $Q = - NkT \ln(\frac{Vf}{Vi})$ .
Adiabatic Compression: $VT^{f/2} = constant$ and $VP^{\gamma} = constant$ , with $\gamma = (f+2)/f$ .
Heat Capacity: $C = \frac{Q}{\Delta T}$ . Constant volume: $CV = (\frac{\partial U}{\partial T})V$ . Constant pressure: $CP = (\frac{\partial H}{\partial T})P = (\frac{\partial U}{\partial T})P + P(\frac{\partial V}{\partial T})P$ . Relationship for ideal gas: $CP = CV + nR$ .
Latent Heat: $L = \frac{Q}{m}$ .
Enthalpy: Definition $H = U + PV$ . For constant pressure process, $\Delta H = Q + W_{other}$ .
Heat conduction is $\frac{Q}{\Delta t} = -kt A \frac{dT}{dx}$ Thermal conductivity \propto T^1/2 -Equipartition thm: Energy of each quadratic DOF is $\frac{1}{2} kT$ . f = #degrees of freedom, $U{thermal} = N f \frac{1}{2} kT$
- Isothermal atmosphere T=const: $P(z) = P(0)e^{-mgz/kT}$