Lecture 49 More on PhaseTransition, binary system? Critical pointTricritical point?Binary system·Osmosis pressure·Mixture
Lecture 49 More on Phase Transition, binary system • Critical point • Tricritical point • Binary system • Osmosis pressure • Mixture
Gibbs' phase rule. The rule applies to non-reactive multi-componentheterogeneous systems in thermodynamicequilibrium and is given by the equalityF=C-P+2·Fisthenumberofdegreesof freedom. C is the number of components· P is the number of phases. The number of degrees of freedom is the numberof independent intensive variables2
Gibbs' phase rule • The rule applies to non-reactive multi-component heterogeneous systems in thermodynamic equilibrium and is given by the equality 𝐹 = 𝐶 − 𝑃 + 2 • 𝐹 is the number of degrees of freedom • 𝐶 is the number of components • 𝑃 is the number of phases • The number of degrees of freedom is the number of independent intensive variables 2
: The composition of each phase is determined byC - 1 intensive variables (such as mole fractions) ineach phase. The total number of variables is (C- 1)P + 2)where the extra two are temperature T andpressurep3
• The composition of each phase is determined by 𝐶 – 1 intensive variables (such as mole fractions) in each phase • The total number of variables is (𝐶– 1)𝑃 + 2, where the extra two are temperature 𝑇 and pressure 𝑝. 3
· Since the phases are in thermodynamic equilibriumwith each other, the chemical potentials of thephases must be equal. The number of equalityrelationships determines the number of degrees offreedom.· Forexample, the equation μlig(T,p) = μvap(T,p),defines temperature as a function of pressure or viceversa. The number of constraints are C(P- 1), since thechemical potential ofeach component must beequal in all phases.. The number of degrees of freedomF = (C-1)P + 2- C(P-1) = C- P + 2X
• Since the phases are in thermodynamic equilibrium with each other, the chemical potentials of the phases must be equal. The number of equality relationships determines the number of degrees of freedom. • For example, the equation 𝜇𝑙𝑖𝑞(𝑇, 𝑝) = 𝜇𝑣𝑎𝑝(𝑇, 𝑝), defines temperature as a function of pressure or vice versa • The number of constraints are 𝐶(𝑃– 1), since the chemical potential of each component must be equal in all phases. • The number of degrees of freedom 𝐹 = (𝐶– 1)𝑃 + 2 – 𝐶(𝑃– 1) = 𝐶 – 𝑃 + 2 4
Pure substances (one component)· For pure substancesC = 1so that F = 3 - P· In a single phase (P = 1)condition, two variables(F = 2), such as temperature and pressure, can bechosenindependentlyto beanypairof valuesconsistentwith the phase.·However,if the temperatureand pressure combinationranges to a point where the pure componentundergoes a separation into two phases (P = 2)F decreases from 2 to 1..When the system enters the two-phase region, itbecomes no longer possible to independently controltemperatureandpressure.5
Pure substances (one component) • For pure substances 𝐶 = 1 so that 𝐹 = 3 – 𝑃 • In a single phase (𝑃 = 1) condition, two variables (𝐹 = 2), such as temperature and pressure, can be chosen independently to be any pair of values consistent with the phase. • However, if the temperature and pressure combination ranges to a point where the pure component undergoes a separation into two phases (𝑃 = 2), 𝐹 decreases from 2 to 1. • When the system enters the two-phase region, it becomes no longer possible to independently control temperature and pressure. 5