Thermal Properties of Matter

• Temperature and Heat

  • Heat
    • Energy transferred due to temperature difference
    • SI Unit: Joule (J) | Practical Unit: Calorie (cal)
  • Temperature
    • Measure of degree of hotness or coldness
    • SI Unit: Kelvin (K)
  • Temperature Scales & Conversion
    • Celsius, Fahrenheit, and Kelvin
    • Conversion Formula: $\frac{C}{5} = \frac{F - 32}{9} = \frac{K - 273.15}{5}$
  • Measurement of Temperature
    • Thermometer: Uses property changes with temperature

• Thermal Expansion

  • Expansion of solids, liquids, and gases upon heating
  • Linear Expansion ($\alpha$)
    • Change in length: $\Delta L = L \alpha \Delta T$
  • Area/Superficial Expansion ($\beta$)
    • Change in area: $\Delta A = A \beta \Delta T$
  • Volume/Cubical Expansion ($\gamma$)
    • Change in volume: $\Delta V = V \gamma \Delta T$
  • Relation Between Coefficients
    • $\alpha : \beta : \gamma = 1 : 2 : 3$
  • Anomalous Expansion of Water
    • Contracts from 0°C to 4°C
    • Maximum density at 4°C
    • Enables aquatic life survival in winter

• Specific Heat Capacity & Calorimetry

  • Heat Capacity ($S$)
    • Heat required to raise temperature of a body by 1 K: $S = \frac{\Delta Q}{\Delta T}$
  • Specific Heat Capacity ($c$)
    • Heat required per unit mass: $\Delta Q = m c \Delta T$
  • Molar Specific Heat Capacity ($C$)
    • Heat required per mole of substance
    • At Constant Volume ($C_v$)
    • At Constant Pressure ($C_p$)
    • Mayer's Relation: $C_p - C_v = R$
  • Calorimetry
    • Science of measuring heat
    • Principle of Calorimetry: Heat Lost = Heat Gained (Conservation of Energy)

• Change of State & Latent Heat

  • Phases of Matter: Solid, Liquid, Gas
  • Phase Transitions
    • Melting / Fusion: Solid to Liquid
    • Vaporization: Liquid to Gas
    • Sublimation: Solid directly to Gas
  • Latent Heat ($L$)
    • Heat absorbed/released during state change at constant temperature
    • Formula: $Q = m L$
    • Latent Heat of Fusion ($L_f$): Solid $\leftrightarrow$ Liquid
    • Latent Heat of Vaporization ($L_v$): Liquid $\leftrightarrow$ Gas
  • Regelation
    • Phenomenon of melting under pressure and refreezing when pressure drops
  • Triple Point
    • Temperature and pressure where solid, liquid, and gas coexist in equilibrium
    • Triple point of water: 273.16 K (0.01°C) at 0.006 atm

• Modes of Heat Transfer

  • Conduction
    • Heat transfer through direct molecular collision without actual bulk movement
    • Occurs predominantly in Solids
    • Rate of Heat Flow ($H$): $H = \frac{KA(T_1 - T_2)}{L}$
    • Thermal Conductivity ($K$): Material's ability to conduct heat
  • Convection
    • Heat transfer by actual physical movement of fluid particles
    • Occurs in Fluids (Liquids and Gases)
    • Natural Convection: Driven by gravity/buoyancy (e.g., Sea breeze, Land breeze)
    • Forced Convection: Driven by pumps or fans
  • Radiation
    • Heat transfer via Electromagnetic Waves (requires no medium)
    • Black Body Radiation: Perfect absorber and emitter of radiation
    • Stefan-Boltzmann Law: Total radiated power $E = \sigma T^4$
    • Wien's Displacement Law: Peak wavelength is inversely proportional to temperature ($\lambda_{max} T = b$)
    • Newton's Law of Cooling: Rate of cooling is proportional to temperature difference ($\frac{dQ}{dt} \propto (T - T_0)$)