Chapter 1: Laws of Thermodynamics

Zeroth Law establishes temperature as a transitive property of thermal equilibrium. First Law (Q = $\Delta U$ + W) is the energy conservation statement for any thermodynamic process. Sign convention: absorbed heat and expansion work are positive; released heat and compression work are negative. Second Law (Kelvin-Planck / Clausius) forbids 100% efficient engines and spontaneous heat flow from cold to hot. It introduces the concept of entropy, which always increases in irreversible processes.

Chapter 2: Thermodynamic Processes

Four standard processes are defined by which quantity is held constant or set to zero:

• Isothermal (T = const): $\Delta U$ = 0; Q = W = nRT ln($V_{2}$/$V_{1}$); PV = const; rectangular hyperbola on PV diagram.
• Adiabatic (Q = 0): W = −$\Delta U$; PV^γ = const; steeper curve than isothermal. Expansion cools, compression heats.
• Isochoric (V = const): W = 0; Q = $\Delta U$ = nCᵥ$\Delta T$; vertical line on PV diagram; P/T = const.
• Isobaric (P = const): W = P$\Delta V$ = nR$\Delta T$; Q = nCₚ$\Delta T$; horizontal line on PV diagram; V/T = const.

Mayer's relation Cₚ − Cᵥ = R connects the two process-specific heats. The work done in any process is the area under the corresponding PV curve, positive for expansion and negative for compression.

Chapter 3: Carnot Engine and Refrigerator

The Carnot cycle — two isothermals + two adiabatics — is the most efficient reversible cycle between $T_{1}$ and $T_{2}$. Efficiency η = 1 − $T_{2}$/$T_{1}$ (temperatures in kelvin). Net work W = $Q_{1}$ − $Q_{2}$. A refrigerator reverses the cycle: COP = $Q_{2}$/W = $T_{2}$/($T_{1}$ − $T_{2}$). Key facts: efficiency < 1 always; COP > 1 is possible; efficiency → 1 only when $T_{2}$ → 0 K (absolute zero, unattainable).

Chapter 4: Kinetic Theory of Gases

Ideal gas: PV = nRT = Nk_BT. Kinetic pressure: P = ⅓ρv_r$ms^{2}$. Three molecular speeds: v_mp = √(2RT/M), v_avg = √(8RT/πM), v_rms = √(3RT/M). Order always: v_mp < v_avg < v_rms.

Chapter 5: Degrees of Freedom and Specific Heats

Equipartition assigns ½RT per mole per degree of freedom. Monoatomic (f = 3): Cᵥ = 3R/2, Cₚ = 5R/2, γ = 5/3. Diatomic (f = 5): Cᵥ = 5R/2, Cₚ = 7R/2, γ = 7/5. Polyatomic (f = 6): Cᵥ = 3R, Cₚ = 4R, γ = 4/3. Internal energy U = (f/2)nRT. Average translational KE per molecule = (3/2)k_BT.