Thermodynamics is the branch of physics that governs energy exchange between systems and their surroundings. THERM-01 covers two deeply connected areas — classical thermodynamics (laws, processes, heat engines) and the kinetic theory of gases (molecular speeds, degrees of freedom, specific heats) — together accounting for 2–3 questions per year in NEET.

The Laws of Thermodynamics

The Zeroth Law establishes the concept of temperature: if system A is in thermal equilibrium with B, and B with C, then A and C are also in thermal equilibrium. This transitive property allows thermometers to function.

The First Law is energy conservation for thermodynamic systems: $Q = \Delta U + W$, where Q is heat absorbed by the system (J), $\Delta U$ is the change in internal energy (J), and W is the work done by the system (J). All three carry dimensions [ML^{2}$$T^{-2}]. NEET sign convention: Q > 0 when heat is absorbed, W > 0 when gas expands (positive work done by gas), and $\Delta U$ > 0 when temperature rises.

The Second Law has two equivalent statements. Kelvin-Planck: no cyclic heat engine can convert all the heat absorbed from a hot reservoir into work — some fraction must always be rejected to a cold reservoir. Clausius: heat cannot spontaneously flow from a cold body to a hot body without external work being supplied. Together these statements mean that perpetual-motion machines of the second kind are impossible and that all real processes are irreversible to some degree.

Four Thermodynamic Processes

Isothermal (T = constant): For an ideal gas, temperature constancy implies $\Delta U$ = 0, so all heat input is converted to work: Q = W = nRT ln($V_{2}$/$V_{1}$). The PV curve is a rectangular hyperbola (PV = constant). Isothermal processes are realised when change is very slow and the system is in contact with a large thermal reservoir.

Adiabatic (Q = 0): No heat is exchanged — realised in perfectly insulated containers or in very rapid processes. Since Q = 0, the First Law gives W = −$\Delta U$, meaning the gas does work entirely at the expense of its internal energy. Adiabatic expansion cools the gas; adiabatic compression heats it. The governing relation is PV^γ = constant (also TV^(γ−1) = constant), and the curve on the PV diagram is a steeper hyperbola than the isothermal through the same point because γ > 1.

Isochoric (V = constant): Volume is fixed, so W = P $\Delta V$ = 0. All heat input changes only the internal energy: Q = $\Delta U$ = nCᵥ$\Delta T$. The process appears as a vertical line on the PV diagram. The gas law reduces to P/T = constant.

Isobaric (P = constant): Pressure is fixed. Work is done: W = P$\Delta V$ = nR$\Delta T$. Heat supplied is Q = nCₚ$\Delta T$, and $\Delta U$ = nCᵥ$\Delta T$. The process appears as a horizontal line on the PV diagram. V/T = constant (Charles's Law).

Mayer's relation connects the two specific heats: Cₚ − Cᵥ = R. This holds for any ideal gas regardless of molecular type. Cₚ > Cᵥ because at constant pressure, the gas must also do work of expansion; extra heat must be supplied compared to the constant-volume case.

Carnot Engine and Refrigerator

The Carnot engine is the theoretical ideal: it operates between a hot reservoir at $T_{1}$ (K) and a cold reservoir at $T_{2}$ (K) through two reversible isothermal and two reversible adiabatic steps. Its efficiency — the highest achievable by any engine between these two temperatures — is $\eta = 1 - \frac{T_2}{T_1} = \frac{W}{Q_1}$. Temperatures must be in kelvin; the single most common NEET error is substituting Celsius values directly.

A refrigerator is the reverse Carnot device: work W is supplied to pump heat $Q_{2}$ from the cold reservoir to the hot reservoir. The coefficient of performance is $\text{COP} = \frac{Q_2}{W} = \frac{T_2}{T_1 - T_2}$. Unlike engine efficiency (always < 1), COP can greatly exceed 1.

Kinetic Theory of Gases

The microscopic basis of thermodynamics is the kinetic theory. For an ideal gas: PV = nRT = Nk_BT, where k_B = $1.38 \times 10^{-23}$ J/K is Boltzmann's constant. The kinetic pressure formula P = ⅓ρv_r$ms^{2}$ connects measurable pressure to molecular root-mean-square speed.

Three characteristic speeds arise from the Maxwell speed distribution: the most probable speed v_mp = √(2RT/M), the mean speed v_avg = √(8RT/πM), and the root-mean-square speed v_rms = √(3RT/M). Their ordering is always v_mp < v_avg < v_rms with the ratio √2 : √(8/π) : √3 ≈ 1 : 1.128 : 1.224.

Degrees of freedom (f) determine how energy is distributed microscopically. Monoatomic gases (He, Ne, Ar) have f = 3 (three translational modes only). Diatomic gases ($O_{2}$, $N_{2}$, $H_{2}$) have f = 5 (three translational + two rotational). Polyatomic nonlinear gases (C$O_{2}$, $H_{2}$O) have f = 6 (three translational + three rotational). By the equipartition theorem, average energy per degree of freedom = ½k_BT per molecule = ½RT per mole. Internal energy is U = (f/2)nRT, specific heats are Cᵥ = (f/2)R and Cₚ = ((f+2)/2)R, giving γ = (f+2)/f: monoatomic γ = 5/3, diatomic γ = 7/5, polyatomic γ = 4/3. The average translational kinetic energy per molecule is always (3/2)k_BT regardless of gas type, which is the microscopic definition of temperature.

NEET Priority Summary: Always convert °C to K for Carnot; remember adiabatic ≠ isothermal (Q = 0 does not mean $\Delta T$ = 0); recall v_mp < v_avg < v_rms; memorise the f-γ table; and use area under PV curve for work.