Physics Chapter 4: Thermal Properties

Chapter 4: Various Thermal Properties

• Specific Heat: Specific heat (C) is the amount of heat required to raise the temperature of one mole of a substance by one degree at constant volume (Cv). Change in internal energy (DE) is equal to DQ (amount of heat) at constant volume.
• Experimental Observation: Dulong-Petit Law states a relationship between specific heat and the atomic weight of a solid; at high temperatures (C = 3R)

Models of Specific Heat

• Classical Model: Assumes that atoms in a solid vibrate harmonically around fixed positions when heated. The energy of one oscillator (in 1 dimension) is equal to kT. The energy of a solid consisting of one mole of N oscillators in 3 dimensions is E = 3NkT = 3RT. Specific heat, Cv, is constant (3R) and independent of temperature.

• Einstein Model: Treats atoms as independent oscillators. Explains specific heat behavior at high temperatures but fails at low. The average energy of an oscillator in 3 Dimensions is E = 3ħω/(e^(ħω/KT) - 1). Specific heat Cv depends on temperature.

• Debye Model: Considers interactions between oscillators, providing a more accurate description of specific heat behavior, especially at low temperatures. Expressed by the average energy of one oscillator E = 3ħω/(e^(ħω/KT) - 1) which ultimately relates to frequency.

High and Low Temperatures

• High Temperature: Experimental specific heat values match the classical model predictions. Cv = 3R
• Low Temperature: Specific heat approaches zero asymptotically for the Debye model, diverging from predictions given by classical models. Cv = 3R (T/ΘD)³

Chapter 5: Electron Theory

• Free Electrons: Electrons inside a metal sample move freely, except at the boundaries.
• Interatomic Interaction: The interaction between conduction electrons and ions or other electrons is weak due to the high speeds of electrons near ions.
• Collisions: The frequency of collisions between conduction electrons and ions is limited due to the short time electrons spend near ions and the resulting reduced likelihood of interactions
• Interaction: The interaction between conduction electrons themselves is weak, as described by the Pauli exclusion principle (parallel spin electrons cannot occupy the same quantum state).

Electrical Conductivity

• Current Density: The relationship between current density (J) and applied electric field (E) is the electrical conductivity
• Relaxation Time: The mean time between collisions of electrons
• Effective Mass: The electron's effective mass influences electrical conductivity.
• Temperature Dependence: Electrical conductivity depends on temperature and the concentration of electrons and effective mass,

Mathiessen's Rule

• Resistivity: The total resistivity of a material is the sum of the contributions from impurities and lattice vibrations (phonon scattering).
• Low Temperature: At low temperatures, the resistivity is dominated by impurities (non-linear)
• High Temperature: At high temperatures, resistivity is dominated by phonon scattering from lattice vibrations.

Explore the various thermal properties including specific heat and its models in this physics chapter. Understand the classical and Einstein models, along with the Dulong-Petit Law that relates specific heat to atomic weight. This quiz will challenge your grasp of fundamental concepts and experimental observations in thermodynamics.