Thermodynamics

• thermodynamics
• chemical thermodynamics
• thermochemistry

Sign conventions

• sign conventions of work $W$:
  • Clausius convention: the work done by the system
    • usually used in physics
    • (used here unless otherwise stated)
  • IUPAC convention: the work done on the system
    • usually used in chemistry

Laws of thermodynamics

• zeroth law of thermodynamics
• first law of thermodynamics
  • $\Delta U=Q-W$ is the change in internal energy of the system, where:
    • $Q$ is the heat added to the system
    • $W$ is the work done by the system
  • (or equivalently $\Delta U=Q+W$, where $W$ is the work done on the system (IUPAC convention))
  • “The internal energy of an isolated system is constant” (Atkins, 2014)
  • for isochoric process: $\Delta U=q_v$
• second law of thermodynamics
  • Clausius statement:
    • “Heat can never pass from a colder to a warmer body without some other change, connected therewith, occurring at the same time” (Wikipedia)
    • “no device is possible whose sole effect is to transfer heat from one system at a temperature $T_{\text{L}}$ into a second system at a higher temperature $T_{\text{H}}$” (Giancoli, 2015)
  • Kelvin-Planck statement: (see: https://en.wikipedia.org/wiki/Second_law_of_thermodynamics#Relation_between_Kelvin’s_statement_and_Planck’s_proposition)
    • “no device is possible whose sole effect is to transform a given amount of heat completely into work” (Giancoli, 2015)
• third law of thermodynamics

Thermodynamic system

(source: commons.wikimedia.org)

• thermodynamic system (or system)

  • closed system
  • open system
  • isolated system

• surroundings

• thermodynamic equilibrium

• thermodynamic state (of a system)

• equation of state

  • $f(p,V,T)=0$
  • e.g., ideal gas law

• state function (פונקציית מצב)

  • examples:
    • internal energy ($U$)
    • enthalpy ($H$)
    • entropy ($S$)
    • pressure ($P$)
      • $P=f(V,T,n)=\frac{nRT}{V}$
    • temperature ($T$)
  • (The differential $dX$ (of a state function $X$) is an exact differential)
    • exact differential describes a change in a state function
    • $\oint dX=0$ (or equivalently ${\int }_{X_1}^{X_2}dX=X_2-X_1$)

• path function (or process function)

  • examples:
    • heat $Q$
    • work $W$
  • inexact differential (a differential whose integral depends on the path taken between two points)
    • (e.g. $\delta W$ and $\delta Q$)

Thermodynamic processes

• thermodynamic processes

• isobaric (אִיזוֹבָּרִי, אחיד-לחץ, קבוע-לחץ)

  • $\Delta P=0$

• isochoric (or isovolumetric) (אִיזוֹכוֹרִי, אחיד-נפח, קבוע-נפח)

  • $\Delta V=0$

• isothermal (איזותרמי, אחיד-טמפרטורה, קבוע-טמפרטורה)

  • $\Delta T=0$

• adiabatic (אַדְיַאבָּטִי)

  • $Q=0$

• isentropic (אִיזֶנְטְרוֹפִּי, אחיד-אנטרופיה, קבוע-אנטרופיה)

• isenthalpic (אִיזֶנְתַּלְפִּי, אחיד-אנתלפייה, קבוע-אנתלפייה)

• quasistatic

• polytropic

• free expansion

  • Joule expansion

• quasi-static process (or quasi-equilibrium process)

• exothermic process and endothermic process

  • exothermic and endothermic reaction

• pressure–volume diagram (or PV diagram)

Spontaneous and nonspontaneous process

• spontaneous process
  • (thermodynamically favorable)
• nonspontaneous process
  • (thermodynamically unfavorable)
• every spontaneous process is irreversible
• spontaneous and nonspontaneous reaction

Reversible and irreversible process

• reversible process (תהליך הפיך)

  • “a process whose direction can be reversed by infinitesimal changes in some properties of the surroundings, such as pressure or temperature” (Wikipedia)
  • reversible heat: $q_{\text{rev}}$
  • see also: Chemical equilibrium

• irreversible process (תהליך לא-הפיך)

• endoreversibility

Work

• thermodynamic work
  • todo https://physics.stackexchange.com/questions/598304/what-does-work-in-thermodynamics-mean-versus-in-other-parts-of-physics
  • pressure-volume work (PV work)
    • $\delta W=PdV$
    • $W=\int PdV$
    • $W=P\Delta V$
      • If the gas expands ($\Delta V>0$) work $W$ is positive. If the gas is compressed ($\Delta V<0$), work $W$ is negative.
    • $P$ is the external pressure (constant)
    • (notice to sign conventions)
  • $W=\int VIdt$

Heat

• heat ($Q$)
  • “the form of energy crossing the boundary of a thermodynamic system by virtue of a temperature difference across the boundary” (Wikipedia)
  • “Energy in transfer between a system and its surroundings by mechanisms other than thermodynamic work and transfer of matter” (Wikipedia)
  • $Q=mc\Delta T=C\Delta T$
  • SI unit: $\mathrm{J}$

Heat capacity

• heat capacity (or thermal capacity) $C$ (קיבול חום)
  • SI unit: $\mathrm{J}\cdot {\mathrm{K}}^{-1}$
• molar heat capacity $c_m=\frac{C}{n}$ (קיבול חום מולי)
  • SI unit: $\mathrm{J}\cdot {\mathrm{K}}^{-1}\cdot \mathrm{mo}{\mathrm{l}}^{-1}$
• specific heat capacity ($c$) (קיבול חום סגולי) is the amount of heat required to raise the temperature of one unit of mass (typically $1\mathrm{kg}$ or $1\mathrm{g}$) of a substance by $1^{\circ }\mathrm{C}$ (or equivalently $1^{\circ }\mathrm{K}$)
  • aka: massic heat capacity or specific heat (חום סגולי)
  • SI unit: $\mathrm{J}\cdot \mathrm{k}{\mathrm{g}}^{-1}\cdot {\mathrm{K}}^{-1}$

Heat transfer

• heat transfer

  • thermal conduction
    • thermal conductivity $\kappa$
    • thermal resistivity $\rho$
  • convection (הסעה)
  • thermal radiation

• thermal equilibrium

  • thermodynamic equilibrium $⟹$ thermal equilibrium

• heating value

• calorimetry (קלורימטריה)

• $q$ is the heat flux

  • SI unit: $W/{\mathrm{m}}^2$
  • $q=\frac{dQ}{dA\cdot dt}$
  • $q=h\Delta T$
  • $h$ is the heat transfer coefficient

Potentials

• thermodynamic potential (or thermodynamic potential energy)
  • internal energy
  • Helmholtz free energy ($A$)
  • enthalpy
  • Gibbs free energy
  • grand potential (or Landau potential) ($\Omega$)
• (thermodynamic) free energy

Internal energy

• internal energy ($U$) (אנרגיה פנימית)
  • in contrast to:
    • macroscopic kinetic energy
    • macroscopic potential energy
      • elastic
      • gravitational
  • for an ideal gas: $U=\frac{f}{2}nRT$
    • $f$ is the degrees of freedom
      • monatomic gas: $f=3$
      • diatomic gas: $f=5$
• change in internal energy ($\Delta U$)
  • first law of thermodynamics
  • for an ideal gas (or real gas with constant presure):
    • $\Delta U=n{C}_{V,m}\Delta T$
    • $n$ is the number of moles
    • $C_{V,m}$ is molar heat capacity at constant volume
    • $\Delta T$ is the change in temperature
  • todo
    • $\Delta U={\sum }_i{p}_i{E}_i$
    • $\Delta U=\sum _i{E}_i$
    • $U=U_{\text{micro,pot}}+U_{\text{micro,kin}}$
    • $\Delta U=\sum U_{\text{products}}-\sum U_{\text{reactants}}$

Enthalpy

• enthalpy (אֶנְתַּלְפִּיָּה)
  • $H=U+PV$
  • SI unit: $\mathrm{J}$
• specific enthalpy
  • $h=H/m$
  • SI unit: $J/kg$
• molar enthalpy
  • $H_m=H/n$
  • SI unit: $J/mol$
• enthalpy change ($\Delta H$) of any process (as chemical reaction, phase transition)
  • SI unit: $\mathrm{J}$ (or $J/mol$ for molar enthalpy change)
  • $\Delta H=H_{\text{final}}-H_{\text{initial}}$
  • examples:
    • enthalpy change of reaction
    • enthalpy of solution
  • $\Delta H=\Delta U+P\Delta V=q_P$
    • $\Delta U$ is the internal energy change
    • $q_P$ is the heat at constant pressure
    • $P\Delta V$ is the PV work
  • $\Delta H>0$ for an endothermic process
  • $\Delta H<0$ for an exothermic process

Gibbs free energy

given constant $T$ and $P$:

• Gibbs free energy (or Gibbs energy)
• $G=U+PV-TS$
  • $T$ is the thermodynamic temperature
• $\Delta G=\Delta H-T\Delta S$
  • the enthalpy contribution is favorable when $\Delta H<0$
  • the entropy contribution is favorable when $\Delta S>0$
• $\Delta H<0\wedge \Delta S>0⟹\Delta G<0$
• $\Delta H>0\wedge \Delta S<0⟹\Delta G>0$
• $\Delta H<0\wedge \Delta S<0⟹\left(T<\frac{\Delta H}{\Delta S}⟺\Delta G<0\right)$
• $\Delta H>0\wedge \Delta S>0⟹\left(T>\frac{\Delta H}{\Delta S}⟺\Delta G<0\right)$
• $\Delta G=0⟺T=\frac{\Delta H}{\Delta S}⟺$ equilibrium
• $\Delta G<0⟺$ spontaneous
• $\Delta G>0⟺$ non-spontaneous
• exergonic and endergonic

Entropy

• entropy ($S$)

• $\Delta S$ refers to the entropy of the system ($\Delta S_{\text{sys}}$)

• entropy change:

  • $\Delta S=\int \frac{d{q}_{\text{rev}}}{T}$
    • $\Delta S=\frac{q_{\text{rev}}}{T}$
      • entropy of fusion: $\Delta S_{\text{fusion}}=\frac{\Delta H_{\text{fusion}}}{T}$
  • $\Delta S_{\text{univ}}=\Delta S_{\text{sys}}+\Delta S_{\text{surr}}$
  • For an ideal gas undergoing an isothermal process:
    • $\Delta S=nR\ln \frac{V_2}{V_1}$

• irreversible process: $\Delta S_{\text{univ}}>0$

• reversible process: $\Delta S_{\text{univ}}=0$

• isolated system: $\Delta S_{\text{surr}}=0$

• non-isolated system: $\Delta S_{\text{surr}}\ne 0$

• for a process $A$:

  • $\Delta S_{\text{univ},A}>0⟺$ process $A$ is spontaneous
  • $\Delta S_{\text{univ},A}=0⟺$ system is at equilibrium
  • $\Delta S_{\text{univ},A}<0⟺$ process $A$ is non-spontaneous
    • there must be a process $B$ coupled to $A$ s.t. $\Delta S_{\text{univ}}=\Delta S_{\text{univ},A}+\Delta S_{\text{univ},B}>0$

Properties of materials

• compressibility (or coefficient of compressibility) (דחיסות)
• thermal expansion (התפשטות תרמית)
  • $\Delta L=\alpha L_0\Delta T$
  • $\Delta V=\beta V_0\Delta T$
• specific heat

misc.

• critical point (or critical state)
  • (e.g., the liquid–vapor critical point)

References

• Atkins, Peter W. (2014). Physical Chemistry. W. H. Freeman.
• Giancoli, Douglas (2015). Physics. Pearson Higher Education & Professional Group.