⚛Molecular Physics Unit 12 – Thermodynamics of Molecular Systems
Thermodynamics in molecular physics explores how heat, work, and energy interact in systems of particles. It covers key concepts like internal energy, enthalpy, entropy, and Gibbs free energy, which help us understand the behavior of gases, liquids, and solids at the molecular level.
The laws of thermodynamics provide a framework for analyzing energy transfer and transformation in molecular systems. Statistical mechanics bridges the gap between microscopic properties and macroscopic behavior, while concepts like phase transitions and chemical equilibrium have practical applications in various fields of science and engineering.
Thermodynamics studies the relationships between heat, work, temperature, and energy in a system
A thermodynamic system is a specific portion of the universe that is being studied, which can be open, closed, or isolated
The surroundings include everything outside the system that can interact with it through the exchange of energy or matter
Thermal equilibrium occurs when two systems in contact have the same temperature and no net heat flow between them
Internal energy (U) represents the total kinetic and potential energy of all particles within a system
Includes translational, rotational, vibrational, and electronic energy contributions
Enthalpy (H) is a state function that equals the internal energy plus the product of pressure and volume (H=U+PV)
Entropy (S) measures the degree of disorder or randomness in a system and always increases in spontaneous processes
Gibbs free energy (G) predicts the spontaneity of a process at constant temperature and pressure (G=H−TS)
Fundamental Laws of Thermodynamics
The zeroth law establishes the concept of thermal equilibrium and provides the basis for temperature measurement
The first law states that energy cannot be created or destroyed, only converted from one form to another
Mathematically expressed as ΔU=Q−W, where Q is heat added and W is work done by the system
The second law introduces entropy and states that the total entropy of an isolated system always increases over time
Implies that heat flows spontaneously from hot to cold objects until thermal equilibrium is reached
The third law states that the entropy of a perfect crystal at absolute zero is zero, providing a reference point for entropy calculations
These laws govern the behavior of thermodynamic systems and set limits on the efficiency of energy conversion processes
Statistical Mechanics Basics
Statistical mechanics connects the microscopic properties of individual atoms and molecules to the macroscopic thermodynamic properties of materials
The Boltzmann distribution describes the probability of a system being in a particular microstate with energy Ei at temperature T
Probability is proportional to e−Ei/kT, where k is the Boltzmann constant
The partition function (Z) is a sum over all possible microstates and relates microscopic properties to macroscopic thermodynamic quantities
Z=∑ie−Ei/kT for a canonical ensemble (fixed N, V, and T)
Thermodynamic properties can be derived from the partition function, such as internal energy (U=−∂lnZ/∂β) and entropy (S=klnZ+kT∂lnZ/∂T)
The equipartition theorem states that each quadratic degree of freedom (translational, rotational, or vibrational) contributes 21kT to the average energy per molecule
Energy and Heat in Molecular Systems
Heat is the transfer of energy between two systems due to a temperature difference, while work is the transfer of energy through organized motion
The heat capacity (C) is the amount of heat required to raise the temperature of a substance by one degree
C=dTdQ, and can be measured at constant volume (CV) or constant pressure (CP)
The molar heat capacity is the heat capacity per mole of a substance and depends on the degrees of freedom available to the molecules
The equipartition theorem predicts that the molar heat capacity of an ideal gas is 21R per quadratic degree of freedom, where R is the gas constant
The Dulong-Petit law states that the molar heat capacity of a solid at high temperatures is approximately 3R, as each atom has three vibrational degrees of freedom
The heat of vaporization and heat of fusion are the amounts of energy required to convert a substance from liquid to gas or solid to liquid, respectively
Entropy and the Second Law
Entropy is a measure of the disorder or randomness in a system and always increases in spontaneous processes
The second law of thermodynamics states that the total entropy of an isolated system always increases over time
The Clausius inequality relates entropy change to heat transfer and temperature: ΔS≥∫TdQ
The Boltzmann equation defines entropy in terms of the number of microstates (Ω) accessible to a system: S=klnΩ
The third law of thermodynamics provides an absolute reference point for entropy, stating that the entropy of a perfect crystal at absolute zero is zero
Entropy drives many processes in molecular systems, such as the mixing of gases, the unfolding of proteins, and the formation of micelles in solution
Thermodynamic Potentials and Free Energy
Thermodynamic potentials are state functions that describe the energy content of a system under different conditions
The internal energy (U) is the total kinetic and potential energy of all particles within a system
Enthalpy (H) is the sum of internal energy and the product of pressure and volume: H=U+PV
Represents the heat content of a system at constant pressure
Helmholtz free energy (A) is the maximum amount of work a system can perform at constant temperature and volume: A=U−TS
Gibbs free energy (G) is the maximum amount of non-expansion work a system can perform at constant temperature and pressure: G=H−TS
The change in Gibbs free energy determines the spontaneity of a process: ΔG<0 for spontaneous processes
The chemical potential (μ) is the change in Gibbs free energy per mole of substance added at constant temperature, pressure, and composition
Phase Transitions and Equilibrium
Phase transitions occur when a substance changes from one state of matter (solid, liquid, or gas) to another
The Gibbs phase rule relates the number of components (C), phases (P), and degrees of freedom (F) in a system at equilibrium: F=C−P+2
The Clapeyron equation describes the slope of a phase boundary in a pressure-temperature diagram: dTdP=TΔVΔH
The Clausius-Clapeyron equation is a special case for the vapor-liquid equilibrium: lnP1P2=−RΔHvap(T21−T11)
The chemical potential of each component is equal in all phases at equilibrium: μiα=μiβ=μiγ
The Gibbs-Duhem equation relates changes in chemical potential to changes in temperature and pressure at equilibrium: SdT−VdP+∑iNidμi=0
Applications in Molecular Physics
Thermodynamics plays a crucial role in understanding the behavior of gases, liquids, and solids at the molecular level
The ideal gas law (PV=nRT) describes the relationship between pressure, volume, temperature, and the number of moles for an ideal gas
The van der Waals equation modifies the ideal gas law to account for intermolecular forces and the finite volume of molecules: (P+V2an2)(V−nb)=nRT
The Langmuir adsorption isotherm describes the adsorption of molecules onto a surface as a function of pressure: 1−θθ=KP
The Gibbs adsorption isotherm relates the change in surface tension to the adsorption of solutes at an interface: dγ=−∑iΓidμi
The Arrhenius equation describes the temperature dependence of reaction rates: k=Ae−Ea/RT, where Ea is the activation energy
The Nernst equation relates the equilibrium potential of an electrochemical cell to the standard potential and the concentrations of reactants and products: E=E0−nFRTlnQ