Connections to Other Physics Topics

Thermodynamics ↔ Mechanics (ME-04 Work-Energy)

• First Law: Q = $\Delta U$ + W is simply energy conservation for a thermodynamic system.
• Work W = ∫P dV in thermodynamics = ∫F dx in mechanics (area under respective graphs).
• Internal energy U = (f/2)nRT is the sum of microscopic kinetic energies.

Thermodynamics ↔ Waves (WAVE-01)

• Speed of sound in a gas: v = √(γP/ρ) = √(γRT/M). This uses the adiabatic bulk modulus (B = γP), NOT the isothermal value, because sound waves are adiabatic compressions and expansions (fast, no time for heat transfer).
• The γ value for the gas directly determines the speed of sound.

Thermodynamics ↔ Electrostatics / EMF

• Heat generated by a resistor (Q = $I^{2}$Rt) enters the First Law as Q in Joule heating problems.

Kinetic Theory ↔ Statistical Physics

• Maxwell speed distribution is the probability distribution of v_mp, v_avg, v_rms.
• The concept of equipartition (½k_BT per DOF) extends to all classical systems.

Adiabatic ↔ Atmosphere

• The lapse rate (drop of temperature with altitude in the atmosphere) results from adiabatic expansion of rising air parcels. This is why mountains are cold.

Summary of Cross-Topic Formula Links