Appunti VERIFICATO
Termodinamica 2
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- Gibbs' Phase Rule:
- For non-reactive systems with
Fphases andCcomponents, the number of degrees of freedom (variance,V) is given byV = C + 2 - F. - This rule quantifies how many intensive variables (like pressure, temperature, or composition) can be independently varied while maintaining phase equilibrium.
- For non-reactive systems with
- Derivation of Phase Rule:
- System Descriptors: A single phase is described by
P,T, andC-1independent molar fractions, totalingC+1intensive variables. ForFphases, there areF(C+1)total variables. - Equilibrium Constraints: Thermal, mechanical, and chemical equilibrium conditions impose
(C+2)(F-1)constraints on the system. - Variance Calculation:
V = F(C+1) - (C+2)(F-1), which simplifies toV = C + 2 - F.
- System Descriptors: A single phase is described by
- Examples of Phase Rule Application:
- For a single component (H2O, C=1):
V=2for one phase,V=1for two coexisting phases, andV=0for three coexisting phases (triple point).
- For a single component (H2O, C=1):
- Systems with Chemical Reactions:
- If
Rindependent chemical reactions occur, the variance is further reduced, and the formula becomesV = C + 2 - F - FR.
- If
- Clapeyron Equation (Monocomponent Systems):
- Describes the
P(T)coexistence curve between two phases (α and β) for a single component (C=1). - Derived from the equality of chemical potentials (
dµα = dµβ) and the Gibbs-Duhem relation (dµ = -SdT + VdP). - The equation is
dP/dT = L / (T(Vα - Vβ)), whereLis the latent heat of transition andΔVis the molar volume change.
- Describes the
- Clausius-Clapeyron Equation (Gas-Phase Approximation):
- A simplification of the Clapeyron equation used when one phase is a gas (e.g., liquid-gas transition).
- It applies two approximations: the gas behaves ideally (
V_gas ≈ RT/P) and its molar volume is significantly larger than the condensed phase (V_gas >> V_condensed). - These approximations lead to
dP/dT = LP / (RT²), which can also be written asd(lnP)/dT = L / (RT²). This is crucial for understanding vapor pressure curves.
- P-V Isotherms and Phase Transition:
- P-V diagrams illustrate phase transitions, showing regions of constant pressure during condensation (e.g., gas to liquid).
- The validity of the ideal gas model at high temperatures and low pressures justifies the approximations used in the Clausius-Clapeyron equation for those conditions.