Thermodynamics & Kinetic Theory
(Prepared for SRMJEEE – Physics)
Goal: Master the fundamentals, solve typical JEE problems, and remember the key formulas.
1. Simple Explanation
| Concept | What It Means |
|---|---|
| Thermodynamics | Study of energy, heat, and work in macroscopic systems. |
| Kinetic Theory | Explains macroscopic gas properties from microscopic molecular motion. |
| State Variables | Properties that depend only on the state (P, V, T, U, S, H, G). |
| Process | Path between two states (isothermal, adiabatic, isobaric, isochoric). |
2. Key Points
2.1 Laws of Thermodynamics
| Law | Statement | Symbols |
|---|---|---|
| 0th | If two systems are each in thermal equilibrium with a third, they are in equilibrium with each other. | Temperature (T) |
| 1st | Energy cannot be created or destroyed: (dU = \delta Q - \delta W). | (U) – internal energy, (Q) – heat added, (W) – work done by system |
| 2nd | Entropy of an isolated system never decreases: (\Delta S \ge 0). | (S) – entropy; ( \delta Q_{\text{rev}} = T, dS) |
| 3rd | As (T \to 0), entropy approaches a constant (often zero). | – |
Useful Consequences
- Heat Engine: Work (W = Q_h - Q_c), efficiency (\eta = \frac{W}{Q_h}).
- Carnot Efficiency: (\eta_{\text{Carnot}} = 1 - \frac{T_c}{T_h}).
- Adiabatic Process: (P V^\gamma = \text{constant}), (TV^{\gamma-1} = \text{constant}).
2.2 Thermodynamic Quantities
| Quantity | Definition | SI Units |
|---|---|---|
| (U) | Internal energy | J |
| (H) | Enthalpy (H = U + PV) | J |
| (S) | Entropy | J/K |
| (G) | Gibbs free energy (G = H - TS) | J |
| (C) | Specific heat (mass basis) | J kg⁻¹ K⁻¹ |
| (C_p, C_v) | Specific heats at constant pressure/volume | J kg⁻¹ K⁻¹ |
2.3 Heat Transfer
| Mode | Equation | When it happens |
|---|---|---|
| Conduction | ( \dot{Q} = \frac{k A \Delta T}{L}) | Solid, temperature gradient |
| Convection | ( \dot{Q} = h A \Delta T) | Fluid motion |
| Radiation | ( \dot{Q} = \varepsilon \sigma A (T^4_{\text{hot}} - T^4_{\text{cold}})) | Hot & cold bodies |
2.4 Calorimetry
- Heat of mixing: (Q = m c (T_f - T_i)).
- Latent heat: (Q = m L).
- Specific heat of a substance: Determined by measuring (Q) for a known temperature change.
2.5 Thermal Expansion
| Type | Formula | Coefficient |
|---|---|---|
| Linear | (\Delta L = \alpha L_0 \Delta T) | (\alpha) |
| Volume | (\Delta V = \beta V_0 \Delta T) | (\beta = 3 \alpha) |
2.6 Kinetic Theory of Gases
| Relation | Derivation (ideal gas) | Key Formula |
|---|---|---|
| Pressure | (P = \frac{1}{3}\rho \bar{v^2}) | (P V = N k_B T) |
| Temperature | ( \frac{1}{2} m \bar{v^2} = \frac{3}{2} k_B T) | (T = \frac{m \bar{v^2}}{3 k_B}) |
| Maxwell–Boltzmann Distribution | Probability density of speeds | (f(v) = 4\pi \left(\frac{m}{2\pi k_B T}\right)^{3/2} v^2 e^{-mv^2/2k_B T}) |
2.7 Ideal Gas Processes (JEE Focus)
| Process | Equation | Work / Heat |
|---|---|---|
| Isothermal (T const) | (PV = \text{const}) | (W = nRT \ln\frac{V_f}{V_i}) , (Q = W) |
| Adiabatic (Q = 0) | (PV^\gamma = \text{const}) | (W = \frac{P_fV_f - P_iV_i}{\gamma-1}) |
| Isochoric (V const) | (P \propto T) | (W = 0), (Q = nC_v \Delta T) |
| Isobaric (P const) | (V \propto T) | (W = P \Delta V), (Q = nC_p \Delta T) |
3. Worked Example
Problem
*A Carnot engine operates between (T_h