Part of THERM-01 — Thermodynamics & Kinetic Theory of Gases

10-Sentence Conceptual Overview: Thermodynamics and Kinetic Theory

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Thermodynamics is governed by three fundamental laws: the Zeroth Law defines temperature through transitivity of equilibrium, the First Law states that Q = ΔU\Delta U + W (energy conservation), and the Second Law forbids 100% efficient heat engines and spontaneous heat flow from cold to hot. Four special processes are defined by what is held fixed or set to zero: isothermal (ΔU\Delta U = 0), adiabatic (Q = 0), isochoric (W = 0), and isobaric (nothing is zero). The Carnot engine is the theoretically most efficient engine between two reservoirs at T1T_{1} and T2T_{2} (kelvin), with efficiency η = 1 − T2T_{2}/T1T_{1}. A refrigerator runs the Carnot cycle in reverse, requiring work input and achieving a COP = T2T_{2}/(T1T_{1}T2T_{2}) that can exceed 1. The adiabatic PV curve is steeper than the isothermal through the same point because PV^γ = const has γ > 1 versus PV = const. Kinetic theory explains gas pressure through molecular motion: P = ⅓ρv_rms2ms^{2}, where v_rms = √(3RT/M). Three molecular speed statistics are ranked v_mp < v_avg < v_rms with a fixed ratio of √2 : √(8/π) : √3 ≈ 1 : 1.128 : 1.224. Degrees of freedom determine specific heats via equipartition: monoatomic f = 3 (γ = 5/3), diatomic f = 5 (γ = 7/5), polyatomic f = 6 (γ = 4/3). Internal energy for n moles is U = (f/2)nRT, and the mean translational kinetic energy per molecule is always (3/2)k_BT. The critical NEET exam point is that Carnot efficiency must be calculated with kelvin temperatures, and adiabatic expansion cools gas whereas isothermal expansion does not change temperature.

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