Phases of Matter:
Matter or substance can exist in three familiar phases that is; solid phase, liquid phase, gaseous phase. Matter of some substances can also exist in two less familiar phases that is; super fluid phase, and plasma phase.
Solid Phase: Molecules are arranged in the closely packed form known as crystal. These molecules can only vibrate about their lattice point.
Liquid Phase: Molecules are close together and they take shape of container. Molecules of liquid, inside its volume, can move from place to place, rotate and vibrate.
Gaseous Phase: Molecules are extensively separated and free to move around freely.
Super fluid: The supercritical (or critical) fluid is the liquid/gas under extreme pressure.
Plasma: Plasma is the gas which is made up of free-floating ions and free electrons.
Phase Diagram:
Three regions for three phases are shown in diagram given below. Solid curves or lines symbolize boundary between two phases like fusion curve is boundary between solid phase and liquid phase. These lines are known as equilibrium lines. Implication of this is that under particular conditions of temperature and pressure, a substance can exist in equilibrium in more than one phase at the same time.
Triple Point: This is point where three equilibrium lines meet as indicated in phase diagram given below. At triple point, solid, liquid, and vapor phases of pure substance coexist in equilibrium. All substances have triple point except Helium.
Triple Point Temperature: this is temperature at which solid, liquid, and vapor phases coexist in equilibrium.
Triple Point Pressure: This is pressure at which solid, liquid, and vapor phases coexist in equilibrium.
Critical Point: This defines conditions of temperature and pressure beyond which it is no longer possible to differentiate liquid from the gas. Point is indicated in phase diagram and region beyond critical point is called as fluid region.
Co-exist Phases:
This is when more than one phase of the substance (like liquid-solid) exist side-by-side in equilibrium at same time. For instance, solid water and liquid water can coexist at 00C along procedure of fusion or melting. Gibbs energy (G) for two coexisting phases α and β of the pure substance are equal.
Phase Transitions:
Phase transition takes place when matter changes from one of the phases of matter to another. Process always involves withdrawal or addition of heat energy from or to matter. Using figure given above as illustration, phase transition takes place whenever any one of the curves in phase diagram is crossed. Phase transition for the pure substance takes place at constant temperature and pressure. Implication of this statement is that, for the pure substance dT = dP =0 during the phase change. Though, extensive thermodynamic coordinates or properties (like Volume) change suddenly because of the phase transition. Internal energy (U), enthalpy (H), and entropy (S) may also change during the phase transition.
Latent Heat, L, during Phase Transition:
Latent heat L is an amount of heat energy per mole which should be added or removed when the substance changes from one phase to another. If phase transition occurs reversibly, heat transfer (i.e. latent heat) per mole for transition from initial phase α to the final phase β is provided by
L = T(Sβ - Sα)
Kinds of Phase Transition:
The three kinds of phase transitions are: first order, second order and lambda phase transitions.
First Order Phase Transition:
Phase transitions which are recognizable with i.e. sublimation, vaporization and fusion are known as first order phase transition. They are known as first order as first order derivatives of Gibbs function are finite.
Thus, for first order phase transition:
The specific heat capacity at constant pressure is infinite; this is due to temperature is constant during phase change (CP = T∂S/∂T|P)
Second Order Phase Transition:
This is a phase transition in which second derivates of Gibbs are finite.
For order phase transition,
The only example of second order phase transition is transition for superconductor from superconducting to normal state in zero magnetic fields.
Lambda phase transition:
For lambda phase transition:
The most interesting example of lambda transition is transition from ordinary liquid helium to super fluid helium at a temperature and corresponding pressure known as a lambda point.
Gibbs Function during Phase Transition:
The Gibbs function G doesn't change during phase transition. For coexisting phases,
dG|T,P = 0
I.e. change in Gibbs at constant temperature and pressure is zero.
Two phases (e.g. liquid-gas) can coexist in equilibrium. For coexisting phases α and β of the pure substance
Gα = Gβ = dGα = dGβ
Gibbs function G is provided by equation:
dG = -SdT + VdP
After replacing values we get:
-SαdT + VαdP = -SβdT + VβdP
Rearranging to get:
dP/dT = (Sβ - Sα)/(Vβ - vα)
Further solving we get:
dP/dT = L(T(vβ - Vα))
This equation is called as Clapeyron's equation.
If solid phase is labeled 1, liquid 2, and gas or vapor phase 3, equation can be written as follows:
For solid - vapor phase transition, we have
(dP/dT)13 = L13/(T(V3 - V1))
Where L13 is latent heat of sublimation.
And for solid - liquid phase transition, we get:
(dP/dT)12 = L12/(V2 - V1)
Where L12 is latent heat of fusion
Usefulness of Clapeyron's Equation:
Equation can be integrated to get the expression for pressure as the function of temperature. If following assumptions holds i.e. if variation in latent heat can be negligible, and if one of the phases is vapor, and if vapor is assumed to be the ideal gas, and if specific volume of liquid or solid is neglected in comparison with that of vapor, the integration can be readily performed.
(dP/dT)23 = L23/T(RT/P)
∫dP/P = L23/R∫dT/T2
Then ln P = -L23/RT + ln constant
Tutorsglobe: A way to secure high grade in your curriculum (Online Tutoring)
Expand your confidence, grow study skills and improve your grades.
Since 2009, Tutorsglobe has proactively helped millions of students to get better grades in school, college or university and score well in competitive tests with live, one-on-one online tutoring.
Using an advanced developed tutoring system providing little or no wait time, the students are connected on-demand with a tutor at www.tutorsglobe.com. Students work one-on-one, in real-time with a tutor, communicating and studying using a virtual whiteboard technology. Scientific and mathematical notation, symbols, geometric figures, graphing and freehand drawing can be rendered quickly and easily in the advanced whiteboard.
Free to know our price and packages for online physics tutoring. Chat with us or submit request at [email protected]
tutorsglobe.com importance of senescence assignment help-homework help by online senescence tutors
Nature of Operating Costing - The major purpose of operating costing is to calculate the cost of the services that are offered by the organization.
Theory and lecture notes of Chi-square goodness-of-fit tests all along with the key concepts of chi-square goodness-of-fit tests, homework help, assignment help. Tutorsglobe offers homework help, assignment help and tutor’s assistance on Chi-square goodness-of-fit tests.
Classification and Characteristics of Organisms tutorial all along with the key concepts of Taxonomic Hierarchy, The Super Kingdoms, The Viruses, Eukaryotae and Five Kingdoms.
tutorsglobe.com significance of natural vegetative propagation assignment help-homework help by online natural methods of vegetative propagation tutors
Theory and lecture notes of Insulated Boundary Conditions all along with the key concepts of differential equations, Insulation, Execution in a linear equation by elimination, boundary conditions in time-dependent. Tutorsglobe offers homework help, assignment help and tutor’s assistance on Insulated Boundary Conditions.
redox titration tutorial all along with the key concepts of experiment, potassium permanganate, requirements, procedure, results, treatments of results
Five-Membered Heterocyclics tutorial all along with the key concepts of Occurrence of five-membered heterocyclics, Naming Five Membered Heterocyclics, General Characteristics of Five Membered Heterocyclics, Thiophene, Furan and Pyrrole and Properties of Pyrrole
Theory and lecture notes of Microeconomics Versus Macroeconomics all along with the key concepts of microeconomics versus macroeconomics, Macroeconomists and Microeconomists. Tutorsglobe offers homework help, assignment help and tutor’s assistance on Microeconomics Versus Macroeconomics.
tutorsglobe.com the stomach assignment help-homework help by online digestion tutors
tutorsglobe.com fixation assignment help-homework help by online dark reactions tutors
Redox Titrations tutorial all along with the key concepts of Theory of redox titrations, Preparation of KMnO4 solution, Computations by using the half-reaction method, Determination of the Mass of Iron in a Ferrous Solution
theory and lecture notes of markov algorithms all along with the key concepts of universal model of computation, algorithm design, recurrent issues and troubles in markov programming, reverse the input string, double the input string, serial binary adder. tutorsglobe offers homework help, assignment help and tutor’s assistance on markov algorithms.
tutorsglobe.com artificial pacemaker assignment help-homework help by online medical lab methods tutors
tutorsglobe.com comparative statics with small changes assignment help-homework help by online comparative statics tutors
1958126
Questions Asked
3689
Tutors
1469098
Questions Answered
Start Excelling in your courses, Ask an Expert and get answers for your homework and assignments!!