Thermodynamics forms the backbone of physical chemistry, exploring energy transfer and transformation. This topic introduces key concepts like systems, state variables, and equilibrium, laying the groundwork for understanding how matter and energy interact on a molecular level.

The first law of thermodynamics, conservation of energy, and various thermodynamic processes are crucial for grasping energy flow in chemical systems. These principles help explain how heat, work, and internal energy are interconnected, setting the stage for deeper thermodynamic analysis.

Thermodynamics: Core Concepts

Systems and Surroundings

• A thermodynamic system is the part of the universe under study
  • Can be a specific object, region, or collection of matter
  • Examples: a gas in a cylinder, a solution in a beaker, a biological cell
• The surroundings are everything else that can interact with the system
  • Includes the immediate vicinity and the rest of the universe
  • Exchanges energy and/or matter with the system
• The system and surroundings are separated by a well-defined boundary
  • Can be real (physical barrier) or imaginary (conceptual division)
  • Classified as open (exchange matter and energy), closed (exchange only energy), or isolated (no exchange)

State Variables and Equilibrium

• State variables are properties that describe the state of a thermodynamic system at equilibrium
  • Depend only on the current state, not on the path taken to reach that state
  • Examples: pressure (P), volume (V), temperature (T), composition (n)
• Thermodynamic equilibrium is a state in which the macroscopic properties of a system remain constant over time
  • No net flow of energy or matter between the system and its surroundings
  • Achieved when the system is isolated or connected to a large reservoir
• Intensive properties are independent of the system size
  • Examples: temperature, pressure, density, specific heat
• Extensive properties depend on the size of the system
  • Examples: volume, mass, entropy, enthalpy
  • Become intensive when divided by the amount of substance (molar properties)

First Law of Thermodynamics: Applications

Conservation of Energy

• The first law of thermodynamics states that the change in internal energy of a system (ΔU) is equal to the heat added to the system (Q) minus the work done by the system (W): ΔU = Q - W
  • Expresses the conservation of energy principle
  • Energy cannot be created or destroyed, only converted from one form to another
• Heat (Q) is the transfer of thermal energy due to a temperature difference
  • Flows from a region of higher temperature to a region of lower temperature
  • Measured in joules (J) or calories (cal)
• Work (W) is the energy transfer due to a force acting through a distance
  • In thermodynamics, often involves changes in volume against an external pressure
  • Measured in joules (J) or liter-atmospheres (L·atm)

Thermodynamic Processes

• Isothermal process: temperature remains constant (ΔT = 0)
  • Change in internal energy is zero (ΔU = 0)
  • Heat added equals work done (Q = W)
  • Example: slow compression or expansion of a gas in a piston-cylinder assembly
• Adiabatic process: no heat exchange between system and surroundings (Q = 0)
  • Change in internal energy equals negative of work done (ΔU = -W)
  • Temperature changes due to work
  • Example: rapid compression or expansion of a gas, as in a diesel engine
• Isobaric process: pressure remains constant (ΔP = 0)
  • Heat added equals change in enthalpy (Q = ΔH)
  • Example: heating or cooling a gas at constant pressure, as in a pressure cooker
• Isochoric (isovolumetric) process: volume remains constant (ΔV = 0)
  • Work done is zero (W = 0)
  • Heat added equals change in internal energy (Q = ΔU)
  • Example: heating or cooling a gas in a rigid container

Heat, Work, and Internal Energy: Interrelationships

Internal Energy

• Internal energy (U) is the total kinetic and potential energy of the particles within a system
  • Includes translational, rotational, vibrational, and electronic energy
  • A state function, depending only on the current state of the system
• The change in internal energy (ΔU) is equal to the heat added (Q) minus the work done (W): ΔU = Q - W
  • In an isolated system, ΔU = 0 (conservation of energy)
  • In a cyclic process, where the system returns to its initial state, ΔU = 0 and Q = W

Heat and Work

• Heat and work are both forms of energy transfer between a system and its surroundings
  • Not state functions, as they depend on the path taken
  • Sign convention: Q > 0 when heat is added to the system, W > 0 when work is done by the system
• Heat capacity (C) is the amount of heat required to raise the temperature of a substance by one degree
  • Specific heat capacity (c) is the heat capacity per unit mass
  • Molar heat capacity (Cm) is the heat capacity per mole of substance
• Work in thermodynamics often involves changes in volume against an external pressure
  • For a reversible process: W = -PexΔV, where Pex is the external pressure
  • For an irreversible process, the work done is less than the reversible case due to friction and other dissipative factors

Enthalpy

• Enthalpy (H) is a state function that combines the internal energy and the product of pressure and volume: H = U + PV
  • Represents the total heat content of a system
  • Change in enthalpy (ΔH) equals heat added at constant pressure: ΔH = QP
• Enthalpy is useful for studying chemical reactions and phase changes
  • Standard enthalpy of formation (ΔH°f) is the enthalpy change when one mole of a compound is formed from its elements in their standard states
  • Standard enthalpy of reaction (ΔH°rxn) is the enthalpy change for a reaction carried out under standard conditions (1 atm, 25°C)
  • Hess's law states that the enthalpy change of a reaction is independent of the route taken, allowing the use of enthalpies of formation to calculate enthalpies of reaction

Ideal Gas Law: Applications

Ideal Gas Equation

• The ideal gas law relates the pressure (P), volume (V), temperature (T), and amount (n) of an ideal gas: PV = nRT
  • R is the universal gas constant: R = 8.314 J/(mol·K) = 0.08206 L·atm/(mol·K)
  • Assumes gas particles have negligible volume, no intermolecular forces, and perfectly elastic collisions
  • Approximates the behavior of many gases under ordinary conditions
• Ideal gas mixtures follow Dalton's law of partial pressures: Ptotal = P1 + P2 + ... + Pn
  • Each gas in the mixture behaves independently
  • The partial pressure of each gas is the pressure it would exert if it occupied the entire volume alone

Gas Laws

• Boyle's law: at constant temperature and amount, pressure is inversely proportional to volume
  • P1V1 = P2V2
  • Example: doubling the volume of a gas at constant temperature halves its pressure
• Charles's law: at constant pressure and amount, volume is directly proportional to absolute temperature
  • V1/T1 = V2/T2
  • Example: heating a gas at constant pressure causes it to expand
• Gay-Lussac's law: at constant volume and amount, pressure is directly proportional to absolute temperature
  • P1/T1 = P2/T2
  • Example: heating a gas in a rigid container increases its pressure
• Combined gas law: relates pressure, volume, and temperature when amount is constant
  • P1V1/T1 = P2V2/T2
  • Combines Boyle's, Charles's, and Gay-Lussac's laws
  • Example: compressing a gas adiabatically (no heat exchange) increases its temperature

Kinetic Molecular Theory

• The kinetic molecular theory (KMT) explains the macroscopic properties of gases in terms of the microscopic behavior of gas particles
  • Particles are in constant, random motion
  • Particles have negligible volume compared to the volume of the container
  • Particles undergo perfectly elastic collisions with each other and the container walls
  • There are no attractive or repulsive forces between particles
• KMT relates the average kinetic energy of gas particles to the absolute temperature: KEavg = (3/2)kT
  • k is the Boltzmann constant: k = 1.38 × 10^-23 J/K
  • At a given temperature, all gases have the same average kinetic energy (equipartition theorem)
• The root-mean-square (rms) speed of gas particles is given by: vrms = √(3RT/M)
  • M is the molar mass of the gas
  • Lighter gases have higher rms speeds at a given temperature
  • Example: hydrogen molecules (H2) move faster than oxygen molecules (O2) at the same temperature

Entropy: Spontaneity of Processes

Entropy and the Second Law

• Entropy (S) is a measure of the disorder or randomness of a system
  • Quantifies the number of microstates (possible arrangements) of a system
  • A state function, depending only on the initial and final states
• The second law of thermodynamics states that the entropy of an isolated system always increases for spontaneous processes
  • Spontaneous processes are irreversible and proceed in the direction of increasing entropy
  • Reversible processes (ideal limit) have no change in entropy
  • Example: heat flows spontaneously from hot to cold, increasing the total entropy
• The change in entropy (ΔS) is equal to the heat transferred (Q) divided by the absolute temperature (T): ΔS = Q/T
  • For a reversible process: ΔS = ∫(dQ/T), where the integral is taken over the path
  • For an irreversible process, the actual entropy change is greater than the reversible case
• The third law of thermodynamics states that the entropy of a perfect crystalline substance approaches zero as the temperature approaches absolute zero
  • Provides a reference point for assigning absolute entropy values
  • Example: at 0 K, a perfect crystal has only one possible microstate (lowest entropy)

Gibbs Free Energy

• The Gibbs free energy (G) combines the effects of enthalpy (H) and entropy (S) to determine the spontaneity of a process at constant temperature and pressure: G = H - TS
  • A state function, depending on the current state of the system
  • Change in Gibbs free energy: ΔG = ΔH - TΔS
• A process is spontaneous when ΔG < 0, non-spontaneous when ΔG > 0, and at equilibrium when ΔG = 0
  • Spontaneity depends on the relative magnitudes of ΔH and TΔS
  • Exothermic processes (ΔH < 0) and processes with increasing entropy (ΔS > 0) are favored
  • Example: ice melts spontaneously at room temperature because the entropy increase (ΔS > 0) outweighs the enthalpy increase (ΔH > 0)
• The standard Gibbs free energy change (ΔG°) is the change in Gibbs free energy for a process occurring under standard conditions (1 atm, 25°C)
  • Related to the equilibrium constant (K) of a reaction: ΔG° = -RT ln K
  • Allows the prediction of the direction and extent of a chemical reaction
  • Example: a reaction with K > 1 (ΔG° < 0) proceeds spontaneously in the forward direction

Statistical Interpretation of Entropy

• The Boltzmann equation relates entropy to the number of microstates (Ω): S = k ln Ω
  • k is the Boltzmann constant: k = 1.38 × 10^-23 J/K
  • Microstates are the possible arrangements of particles in a system
  • Example: a gas has more microstates (higher entropy) than a solid at the same temperature
• The statistical interpretation of entropy provides a molecular basis for the second law of thermodynamics
  • A system tends to evolve towards the state with the highest probability (most microstates)
  • Spontaneous processes increase the total number of microstates of the system and surroundings
  • Example: the expansion of a gas into a vacuum is spontaneous because it increases the number of possible particle arrangements
• The Gibbs entropy formula expresses the entropy of a system in terms of the probabilities of its microstates: S = -k Σ pi ln pi
  • pi is the probability of the system being in microstate i
  • Applies to systems with distinguishable particles (e.g., solids, liquids)
  • Example: a perfect crystal at 0 K has only one microstate (p1 = 1, S = 0)