Thermodynamics: every key term you need (+ practice quiz)

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Thermodynamics

Study of heat, temperature, energy. First law: energy conserved. Second law: entropy increases.

Temperature vs Heat

Temperature: measure of kinetic energy of particles (K or °C). Heat: energy transferred due to temperature difference.

Heat Capacity

Energy needed to raise temperature by 1°C. Q = mcΔT where c = specific heat. Varies by material.

Phase Changes

Solid→liquid (melting), liquid→gas (vaporization). Require latent heat; temperature constant during change.

Thermal Equilibrium

Heat flows from hot to cold until temperatures equal. No net heat flow at equilibrium.

First Law of Thermodynamics

ΔU = Q - W. Change internal energy = heat added - work done by system. Energy conserved.

Work in Thermodynamics

W = PΔV. Work done by gas expanding against external pressure. Expansion (positive V) = positive work.

Ideal Gas Law

PV = nRT where n = moles, R = constant, T = absolute temperature (K). Relates pressure, volume, temperature.

Isothermal Process

Constant temperature; ΔU = 0. Q = W. Example: slow expansion/compression.

Adiabatic Process

No heat exchange (Q=0); ΔU = -W. Rapid compression/expansion. Temperature changes without heat.

Entropy

Measure of disorder; increases in spontaneous processes. Second law: total entropy increases (universe becomes more disordered).

Unit 2 Summary

Heat transfers energy. First law conserves total energy. Phase changes occur at constant temperature. Entropy increases.

Kinetic Theory: Average KE

For an ideal gas the average translational kinetic energy per molecule is (3/2)k_BT, independent of molecular mass. Temperature is a measure of average kinetic energy, not total energy.

RMS Speed

v_rms = √(3k_BT/m) = √(3RT/M). At the same temperature, lighter molecules move faster; hydrogen at 300 K has v_rms ≈ 1900 m/s while oxygen has ≈ 480 m/s.

Maxwell–Boltzmann Distribution

Speeds in a gas spread over a skewed curve; heating flattens and shifts the peak right, keeping total area (number of molecules) constant. High-speed tail explains evaporation and escape of light gases.

Pressure from Molecular Collisions

Gas pressure is the average momentum transfer per unit area per second from molecules bouncing off walls. Doubling speed doubles both momentum per hit and hit rate, so P ∝ v² ∝ T at fixed V.

Work as Area Under P–V Curve

W_by gas = ∫P dV = area under the path. Sign convention in AP: W done ON the gas is positive in ΔU = Q + W, so compression adds energy and expansion removes it.

Isobaric Process

Constant pressure: W_on = −PΔV, and Q = nC_pΔT with C_p = C_v + R. Part of the heat does expansion work, so more heat is needed per degree than at constant volume.

Isochoric (Isovolumetric) Process

Constant volume: no work is done, so ΔU = Q entirely. For a monatomic gas ΔU = (3/2)nRΔT; the P–V path is a vertical line.

Internal Energy of Monatomic Gas

U = (3/2)nRT = (3/2)PV. Depends only on temperature (state function), so ΔU is the same for any path between two states while Q and W depend on the path.

Cyclic Processes

Returning to the initial state gives ΔU = 0, so Q_net = −W_on = W_by. Net work equals the enclosed area on the P–V diagram: clockwise = engine (positive net work out), counterclockwise = refrigerator.

Heat Engine Efficiency

e = W_net/Q_hot = 1 − Q_cold/Q_hot. Carnot limit e_max = 1 − T_cold/T_hot with Kelvin temperatures. No real engine reaches Carnot; friction and finite ΔT create entropy.

Second Law (Entropy Statement)

Total entropy of an isolated system never decreases; heat flows spontaneously hot → cold because that raises total entropy (ΔS = Q/T is larger for the cold body gaining heat than for the hot body losing it).

Thermal Conduction Rate

Q/Δt = kAΔT/L. Rate scales with area and temperature difference, inversely with thickness. In series layers, the same Q/Δt passes through each layer, so ΔT splits in proportion to L/k.

Thermal Expansion

ΔL = αL₀ΔT for solids; volume coefficient β ≈ 3α. Holes expand along with the material — a heated ring's hole gets bigger, not smaller.

Adiabatic vs Isothermal Curves

On a P–V diagram an adiabat is steeper than an isotherm through the same point, because in adiabatic expansion the gas also cools, dropping pressure faster than PV = const alone would.

Free Expansion

Gas expanding into vacuum does no work and exchanges no heat, so ΔU = 0 and T is unchanged for an ideal gas, yet entropy increases — an irreversible process with no P–V path.