Thermodynamics: Basic Concepts and Zeroth Law

• Thermodynamics is the study of energy, its transformations, and its relation to matter

Basic Concepts

• System: Part of the universe under study
• Surroundings: Everything outside the system
• Boundary: Surface separating the system from its surroundings
• Types of systems:
  • Isolated system: No exchange of matter or energy with the surroundings.
  • Closed system: Exchange of energy but not matter with the surroundings.
  • Open system: Exchange of both matter and energy with the surroundings.
• Thermodynamic properties: Macroscopic properties of a system such as temperature (T), pressure (P), and volume (V).
• State of a system: Defined by the values of its macroscopic properties.
• Thermodynamic process: A change in the state of a system.
• Thermodynamic equilibrium: State where macroscopic properties are uniform throughout the system and do not change with time. Includes thermal, mechanical, and chemical equilibrium.

Zeroth Law of Thermodynamics

• If two systems are separately in thermal equilibrium with a third system, then they are also in thermal equilibrium with each other.
• This law introduces the concept of temperature as a fundamental property that determines thermal equilibrium.

First Law of Thermodynamics

• The change in internal energy (ΔU) of a system is equal to the heat added to the system (Q) minus the work done by the system (W): ΔU = Q - W.
• Internal energy (U) is a state function, dependent only on the current state of the system, not on how it reached that state.
• Heat (Q) is the transfer of energy due to temperature difference.
• Work (W) is the transfer of energy by any other means than temperature difference, like a force acting through a distance.
• For an isolated system, ΔU = 0, meaning energy is conserved.

Types of Processes

• Isothermal process: Occurs at constant temperature (ΔT = 0).
  • For an ideal gas, ΔU = 0, so Q = W.
• Adiabatic process: No heat exchange with the surroundings (Q = 0).
  • ΔU = -W.
• Isobaric process: Occurs at constant pressure (ΔP = 0).
  • W = PΔV.
• Isochoric process: Occurs at constant volume (ΔV = 0).
  • W = 0, so ΔU = Q.
• Cyclic process: The system returns to its initial state.
  • ΔU = 0, so Q = W.

Second Law of Thermodynamics

• It is impossible to construct a device that operates in a cycle and produces no effect other than the transfer of heat from a colder body to a hotter body (Clausius statement).
• It is impossible to construct a device that operates in a cycle and converts heat completely into work without transferring some heat to a colder body (Kelvin statement).
• Introduces the concept of entropy (S), a measure of the disorder or randomness of a system.
• For a reversible process, the change in entropy is given by ΔS = Q/T.
• For an irreversible process, ΔS > Q/T.
• The total entropy of an isolated system always increases or remains constant in a reversible process (ΔS ≥ 0).

Heat Engines

• A device that converts thermal energy into mechanical work.
• Operates in a cyclic process.
• Efficiency (η) is the ratio of the work done to the heat absorbed: η = W/QH = (QH - QC)/QH = 1 - (QC/QH), where QH is the heat absorbed from the hot reservoir and QC is the heat rejected to the cold reservoir.
• Carnot engine: A theoretical engine operating in a Carnot cycle, which consists of two isothermal processes and two adiabatic processes.
• Carnot efficiency: The maximum possible efficiency for a heat engine operating between two temperatures: ηCarnot = 1 - (TC/TH), where TC is the absolute temperature of the cold reservoir and TH is the absolute temperature of the hot reservoir.

Refrigerators and Heat Pumps

• A refrigerator transfers heat from a cold reservoir to a hot reservoir, requiring work input.
• A heat pump transfers heat from a cold reservoir to a hot reservoir.
• Coefficient of Performance (COP) for a refrigerator: COP = QC/W, where QC is the heat removed from the cold reservoir and W is the work input.
• COP for a heat pump: COP = QH/W, where QH is the heat delivered to the hot reservoir and W is the work input.
• For a Carnot refrigerator/heat pump: COPCarnot,refrigerator = TC/(TH - TC) and COPCarnot,heat pump = TH/(TH - TC).

Third Law of Thermodynamics

• As the temperature approaches absolute zero (0 K), the entropy of a system approaches a minimum or zero value.
• It is impossible to reach absolute zero in a finite number of steps.

Thermodynamic Potentials

• Internal Energy (U): Energy associated with the microscopic components of a system. U = U(S, V, N), where S is entropy, V is volume, and N is the number of particles.
• Enthalpy (H): H = U + PV. H = H(S, P, N). Useful for constant pressure processes.
• Helmholtz Free Energy (F): F = U - TS. F = F(T, V, N). Useful for constant temperature and volume processes.
• Gibbs Free Energy (G): G = U + PV - TS = H - TS. G = G(T, P, N). Useful for constant temperature and pressure processes, especially phase transitions and chemical reactions.

Maxwell's Relations

• Mathematical relationships derived from the thermodynamic potentials that relate changes in thermodynamic properties.
• Useful for calculating properties that are difficult to measure directly.
• Examples:
  • (∂T/∂V)S,N = -(∂P/∂S)V,N
  • (∂T/∂P)S,N = (∂V/∂S)P,N
  • (∂S/∂V)T,N = (∂P/∂T)V,N
  • -(∂S/∂P)T,N = (∂V/∂T)P,N

Phase Transitions

• A transition between different physical states of matter (solid, liquid, gas, plasma).
• First-order phase transition: Involves a latent heat (heat absorbed or released during the transition) and a discontinuity in the first derivative of the Gibbs free energy (e.g., melting, boiling).
• Second-order phase transition: No latent heat, but a discontinuity in the second derivative of the Gibbs free energy (e.g., change in magnetization in a ferromagnet).
• Clausius-Clapeyron equation: Describes the relationship between pressure and temperature along a phase boundary: dP/dT = L/(TΔV), where L is the latent heat and ΔV is the change in volume during the phase transition.