Heat and Thermodynamics

• Heat: Form of energy transferred between systems due to temperature difference
• Temperature: Measure of average kinetic energy of molecules
• Thermal Equilibrium: When two systems have same temperature, no heat flows
• Zeroth Law of Thermodynamics: If A=B and B=C, then A=C (basis of temperature measurement)

2. Heat Transfer

• Conduction: Heat transfer through molecular collisions without material movement
  Rate: \( \frac{Q}{t} = kA \frac{\Delta T}{d} \)
• Convection: Heat transfer by actual movement of material
• Radiation: Heat transfer through electromagnetic waves, doesn’t require mediumStefan-Boltzmann Law: \( P = \epsilon \sigma A T^4 \)

3. Thermal Expansion

• Linear Expansion: \( L = L_0 (1 + \alpha \Delta T) \)
• Area Expansion: \( A = A_0 (1 + \beta \Delta T) \), where \( \beta = 2\alpha \)
• Volume Expansion: \( V = V_0 (1 + \gamma \Delta T) \), where \( \gamma = 3\alpha \)
• Anomalous expansion of water: Maximum density at 4°C

4. Calorimetry

• Specific Heat Capacity (c): Heat required to raise temperature of unit mass by 1°C\( Q = mc\Delta T \)
• Heat Capacity (C): \( C = mc \)
• Latent Heat: Heat required for phase change at constant temperature\( Q = mL \)
• Principle of Calorimetry: Heat lost = Heat gained (assuming no heat loss to surroundings)

5. Laws of Thermodynamics

• First Law: \( \Delta U = Q – W \) (Conservation of energy)Where \( \Delta U \) = change in internal energy, Q = heat supplied, W = work done by system
• Second Law:
  • Kelvin-Planck: No cyclic process can convert heat entirely into work
  • Clausius: Heat cannot flow from colder to hotter body by itself
• Third Law: Absolute zero (0 K) cannot be achieved

6. Thermodynamic Processes

• Isochoric: Constant volume, W = 0
• Isobaric: Constant pressure, W = \( P\Delta V \)
• Isothermal: Constant temperature, \( \Delta U = 0 \)
• Adiabatic: No heat exchange, Q = 0
• Cyclic Process: \( \Delta U = 0 \), Q = W

7. Kinetic Theory of Gases

• Pressure: \( P = \frac{1}{3} \rho \overline{v^2} = \frac{1}{3} \frac{M}{V} \overline{v^2} \)
• RMS speed: \( v_{rms} = \sqrt{\frac{3RT}{M}} = \sqrt{\frac{3PV}{M}} = \sqrt{\frac{3kT}{m}} \)
• Average kinetic energy per molecule: \( \frac{1}{2} m \overline{v^2} = \frac{3}{2} kT \)
• Internal energy of ideal gas: \( U = \frac{f}{2} nRT \) (f = degrees of freedom)

8. Heat Engines & Refrigerators

• Heat Engine Efficiency: \( \eta = \frac{W}{Q_H} = 1 – \frac{Q_C}{Q_H} \)
• Carnot Engine Efficiency: \( \eta = 1 – \frac{T_C}{T_H} \)
• Refrigerator Coefficient of Performance: \( COP = \frac{Q_C}{W} = \frac{Q_C}{Q_H – Q_C} \)
• Carnot Refrigerator COP: \( COP = \frac{T_C}{T_H – T_C} \)