Fundamentals Of Thermodynamics

Concept

Thermodynamics Fundamentals

1. Nature and Scope

Thermodynamics quantifies energy transformations in physical systems. It does not depend on microscopic detail; it describes macroscopic averages that obey conservation and equilibrium laws.

A system is a quantity of matter or a region in space chosen for study. Everything else is the surroundings. A boundary separates system and surroundings. It may be fixed or moving, real or imaginary.

  • Closed system (control mass): fixed mass, energy may cross.
  • Open system (control volume): mass and energy cross boundaries.
  • Isolated system: no interaction with surroundings.

State, Property, and Process

A property is any measurable or calculable quantity describing a system at equilibrium (e.g., (P,V,T,U,H,S)(P, V, T, U, H, S)). A state is the set of all property values at an instant. A process is a path between states. A cycle returns to its initial state.

For equilibrium, intensive properties (e.g., (T,P)(T, P)) are uniform in space and time. Nonequilibrium thermodynamics handles deviations, but this document assumes local equilibrium.

2. Forms of Energy

All energy interactions reduce to three macroscopic types:

  1. Kinetic energy (motion of mass center): Ek=12mv2E_k = \frac{1}{2} m v^2

  2. Potential energy (position in a force field): Ep=mgzE_p = m g z

  3. Internal energy (U) (microscopic energy):

    • Translational, rotational, vibrational of molecules.
    • Intermolecular potential energy.
    • Electronic excitation, chemical bonds, nuclear binding.

For a system: Etotal=U+Ek+EpE_{total} = U + E_k + E_p

3. System Interactions

Work ( δW\delta W )

Work is energy transfer associated with a generalized force acting through a generalized displacement.

Infinitesimal form: δW=F dx=P dV=τ dθ=E dq\delta W = F\,dx = P\,dV = \tau\,d\theta = E\,dq

For a quasi-static (reversible) expansion: δW=PextdV\delta W = P_{ext} dV Sign convention: work done by the system is positive.

Heat ( δQ\delta Q )

Heat is energy transfer driven by temperature difference. It is path-dependent, like work, not a property.

Positive when into the system.

4. Zeroth Law of Thermodynamics

If body A is in thermal equilibrium with body B, and B with C, then A and C are in equilibrium. This defines a scalar property, temperature, which establishes transitivity of equilibrium and enables thermometry.

5. Property Relations and Exact Differentials

A property’s differential is exact; a path function’s is not.

For property (UU): dU=(∂U∂T)VdT+(∂U∂V)TdVdU = \left( \frac{\partial U}{\partial T} \right)_V dT + \left( \frac{\partial U}{\partial V} \right)_T dV and ∮dU=0\oint dU = 0.

For work or heat:

\ne 0, \quad \oint \delta Q \ne 0 $$ --- ## 6. First Law of Thermodynamics Energy is conserved. For any system: $$ \Delta E = Q - W $$ For a closed system with negligible kinetic and potential energy changes: $$ \Delta U = Q - W $$ For a steady-flow open system (control volume): $$ \dot{Q} - \dot{W} = \dot{m}\left(h_2 - h_1 + \frac{v_2^2 - v_1^2}{2} + g(z_2 - z_1)\right) $$ where $(h = u + Pv)$ is **specific enthalpy**. --- ## 7. Second Law (Preview) The first law quantifies energy, not direction. The second law introduces **entropy** (S), defining feasible processes. For any process: $$ \Delta S_{total} = \Delta S_{system} + \Delta S_{surroundings} \ge 0 $$ Equality holds for reversible processes. --- ## 8. Equilibrium Criteria A system at equilibrium has no unbalanced potential gradients. | Type | Criterion | Example | | ---------- | ------------------------- | ----------------------- | | Thermal | uniform (T) | no heat flow | | Mechanical | uniform (P) | no net force | | Phase | equal chemical potentials | phase coexistence | | Chemical | minimal Gibbs free energy | equilibrium composition | At equilibrium, the total potential energy of the system is stationary ($\delta G = 0$ for constant $T,P$). --- ## 9. Equation of State A **substance model** provides the link between thermodynamic properties: $$ f(P, v, T) = 0 $$ * Ideal gas: $Pv = RT$ * Real gas: use compressibility factor ($Z = Pv/RT$) * Tabulated data: steam tables, equations like Van der Waals, Redlich–Kwong. --- ## 10. Differential Forms and Cyclic Integrals For any infinitesimal process: $$ \delta Q = dU + \delta W $$ Integrating over a cycle: $$ \oint \delta Q = \oint \delta W $$ This defines **mechanical equivalence of heat** (Joule’s experiments). --- ## 11. State Postulates For a simple compressible system, two independent intensive properties fix the state: $$ f(P, v, T) = 0 \quad \text{→ any two of } (P, v, T) \text{ define the third.} $$ If additional effects (electric, magnetic, surface tension, chemical composition) exist, more properties are needed. --- ## 12. Reversibility and Irreversibility A process is **reversible** if both system and surroundings can return to their initial states without net effect. Irreversibility arises from: * Friction * Unrestrained expansion * Mixing * Finite temperature gradients * Inelastic deformation * Chemical reactions For infinitesimal reversible changes: $$ \delta Q_{rev} = T\,dS $$ --- ## 13. Units and Conventions | Quantity | Symbol | SI Unit | Derived Form | | ----------------- | ------- | ------- | ------------ | | Pressure | P | Pa | N/m² | | Temperature | T | K | — | | Energy | E, Q, W | J | N·m | | Specific volume | v | m³/kg | 1/ρ | | Specific enthalpy | h | J/kg | u + Pv | | Specific entropy | s | J/kg·K | — | --- ## 14. References * Çengel & Boles, *Thermodynamics: An Engineering Approach* * Moran & Shapiro, *Fundamentals of Engineering Thermodynamics* * Sonntag & Borgnakke, *Introduction to Engineering Thermodynamics* * Callen, *Thermodynamics and an Introduction to Thermostatistics* ---