[permalink] [id link]
In the first-order phase transition the range of (< i > P, V, T </ i >), where the liquid phase and the gas phase are in equilibrium, it does not exhibit the empirical fact that < var > p </ var > is constant as a function of < i > V </ i > for a given temperature: although this behavior can be easily inserted into the van der Waals model ( see Maxwell's correction below ), the result is no longer a simple analytical model, and others ( such as those based on the principle of corresponding states ) achieve a better fit with roughly the same work.
from
Wikipedia
Some Related Sentences
first-order and phase
Interestingly, experimental evidence indicates that this phase forms by a first-order transition.
Some people consider glass to be a liquid due to its lack of a first-order phase transition
The metastability concept originates in the physics of first-order phase transitions later to acquire new meanings in the study of aggregated subatomic particles ( in atomic nuclei or in atoms ) or in molecules, macromolecules or clusters of atoms and molecules.
This characterizes the process of melting as a first-order phase transition.
Figure 1 ( a ): The Bode plot for a first-order ( one-pole ) highpass filter ; the straight-line approximations are labeled " Bode pole "; phase varies from 90 ° at low frequencies ( due to the contribution of the numerator, which is 90 ° at all frequencies ) to 0 ° at high frequencies ( where the phase contribution of the denominator is − 90 ° and cancels the contribution of the numerator ).
Figure 1 ( b ): The Bode plot for a first-order ( one-pole ) lowpass filter ; the straight-line approximations are labeled " Bode pole "; phase is 90 ° lower than for Figure 1 ( a ) because the phase contribution of the numerator is 0 ° at all frequencies.
The Hamiltonian method differs from the Lagrangian method in that instead of expressing second-order differential constraints on an n-dimensional coordinate space ( where n is the number of degrees of freedom of the system ), it expresses first-order constraints on a 2n-dimensional phase space.
This is a first-order thermodynamic phase transition, which means that, as long as solid and liquid coexist, the equilibrium temperature of the system remains constant and equal to the melting point.
There are still some thermal and magnetic hysteresis problems to be solved for these first-order phase transition materials that exhibit the GMCE to become really useful ; this is a subject of current research.
* structural ( order-disorder, first-order ) phase transitions, and spontaneous symmetry breaking such as
Baryogenesis within the Standard Model requires the electroweak symmetry breaking be a first-order phase transition, since otherwise sphalerons wipe off any baryon asymmetry that happened up to the phase transition, while later the amount of baryon non-conserving interactions is negligible.
This is analogous to metastability for first-order phase transitions.
On the basis of the Virial Theorem, he recognized that this transition should be first-order and should, where the phase transition occurs at too low a temperature for atomic diffusion, result in lattice instabilities.
* A baryon net excess can be created during the electroweak symmetry breaking can be later preserved only if this phase transition was first-order.
This is because in a second-order phase transition sphalerons would wipe off any baryon asymmetry as it is created, while in a first-order phase transition sphalerons would wipe off baryon asymmetry only in the unbroken phase.
the slope field is an array of slope marks in the phase space ( in any number of dimensions depending on the number of relevant variables ; for example, two in the case of a first-order linear ODE, as seen to the right ).
first-order and transition
Precise expressions for the transition probability, based on first-order perturbation Hamiltonians, can be found in Thompson and Baker.
The volume change at the transition point is either discrete ( as in a first-order Ehrenfest transition ) or continuous ( second order Ehrenfest analogy ), depending on the degree of ionization of the gel and on the solvent composition.
first-order and range
A theory about some topic is usually first-order logic together with: a specified domain of discourse over which the quantified variables range, finitely many functions which map from that domain into it, finitely many predicates defined on that domain, and a recursive set of axioms which are believed to hold for those things.
While many simple mechanisms are completely first-order, most complex mechanisms are only first-order within a range of operation.
For example, in an interpretation of first-order logic, the domain of discourse is the set of individuals that the quantifiers range over.
Boolos argued that if one reads the second-order variables in monadic second-order logic plurally, then second-order logic can be interpreted as having no ontological commitment to entities other than those over which the first-order variables range.
Intensional logic is an approach to predicate logic that extends first-order logic, which has quantifiers that range over the individuals of a universe ( extensions ), by additional quantifiers that range over terms that may have such individuals as their value ( intensions ).
Systematic use of this method allows arbitrary computations on given quantities to be replaced by equivalent computations on their affine forms, while preserving first-order correlations between the input and output and guaranteeing the complete enclosure of the joint range.
first-order and i
The asks for an algorithm that takes as input a statement of a first-order logic ( possibly with a finite number of axioms beyond the usual axioms of first-order logic ) and answers " Yes " or " No " according to whether the statement is universally valid, i. e., valid in every structure satisfying the axioms.
Proof: Fix a first-order language L, and let Σ be a collection of L-sentences such that every finite subcollection of L-sentences, i ⊆ Σ of it has a model.
( i ) The upward slope implies that the person feels that more is better: a larger amount received yields greater utility, and for risky bets the person would prefer a bet which is first-order stochastically dominant over an alternative bet ( that is, if the probability mass of the second bet is pushed to the right to form the first bet, then the first bet is preferred ).
This system of rules can be shown to be both sound and complete with respect to first-order logic, i. e. a statement follows semantically from a set of premises iff the sequent can be derived by the above rules.
They are generally weaker than LK ( i. e., they have fewer theorems ), and thus not complete with respect to the standard semantics of first-order logic.
where Δ is the first-order forward-difference operator, i. e.
Being based upon first-order logic, knowledge expressed using one variant of OWL can be logically processed, i. e., inferences can be made upon it.
* the formalism is logically founded, i. e., it has a semantics in first-order logic and the inference mechanisms are sound and complete with respect to deduction in first-order logic,
At that time what were called Pfaffian systems ( i. e. first-order differential equations given as 1-forms ) were in general use ; by the introduction of fresh variables for derivatives, and extra forms, they allowed for the formulation of quite general PDE systems.
Consider the first-order differential operators D < sub > i </ sub > to be infinitesimal operators on Euclidean space.
Essentially, one splits the output of the fiber into two principal polarizations ( usually those with dτ dω = 0, i. e. no first-order variation of time-delay with frequency ), and applies a differential delay to bring them back into synch.
We want to transform this linear first-order PDE into an ODE along the appropriate curve ; i. e. something of the form
Two structures M and N of the same signature σ are elementarily equivalent if every first-order sentence ( formula without free variables ) over σ is true in M if and only if it is true in N, i. e. if M and N have the same complete first-order theory.
A class K of structures of a signature σ is called an elementary class if there is a first-order theory T of signature σ, such that K consists of all models of T, i. e., of all σ-structures that satisfy T. If T can be chosen as a theory consisting of a single first-order sentence, then K is called a basic elementary class.
Atomic or simple molecular desorption will typically be a first-order process ( i. e. a simple molecule on the surface of the substrate desorbs into a gaseous form ).
The structure has no possible mechanisms, i. e. nodal displacements, compatible with zero member extensions, at least to a first-order approximation.
When the chosen time period corresponds to, the fraction of the population that will break down in each time period will be exactly ½ the amount present at the start of the time period ( i. e. the time period corresponds to the half-life of the first-order reaction ).
0.231 seconds.