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physical state

a substance's physical condition; is defined by its physical properties

mechanical equilibrium

the condition of equality of pressure on either side of a shared movable wall

equation of state

an equation that interrelates the variables that define the state of a substance

limiting law

Boyle's and Charles's Laws are examples of this. a law that is strictly true only in a certain limit, in this case p â†’ 0

isotherm

a line in a graph that corresponds to a single temperature

isobar

a line in a graph that corresponds to a single pressure

isochore

a line in a graph that corresponds to a single volume

perfect gas

a gas that obeys the perfect gas law under all conditions

daltonâ€™s law

states that the pressure exerted by a mixture of (perfect) gases is the sum of the pressures that each one would exert if it occupied the container alone

kinetic model

for a gas, considers only the contribution to the energy from the kinetic energies of the molecules

root-mean-square speed

Important results from the model include expressions for the pressure and this. speed V of the molecules of an ideal gas is given by the expression, v=sqrt(3RTM)

Maxwellâ€“Boltzmann distribution of speeds

gives the fraction of molecules that have speeds in a specified range

collision frequency

the average number of collisions made by a molecule in an interval divided by the length of the interval

mean free path

the average distance a molecule travels between collisions

compression factor

The extent of deviations from perfect behaviour is summarized by introducing this. it is a measure of how much the thermodynamic properties of a real gas deviate from those expected of an ideal gas

virial equation

an empirical extension of the perfect gas equation that summarizes the behaviour of real gases over a range of conditions

critical behaviour

The isotherms of a real gas introduce this concept. the physics of critical points.

critical temperature

A gas can be liquefied by pressure alone only if its temperature is at or below this point

van der Waals equation

a model equation of state for a real gas expressed in terms of two parameters, one representing molecular attractions and the other representing molecular repulsions. captures the general features of the behaviour of real gases, including their critical behaviour

reduced variables

The properties of real gases are coordinated by expressing their equations of state in terms of these

work

the process of achieving motion against an opposing force

energy

the capacity to do work

exothermic process

a process that releases energy as heat

endothermic process

a process in which energy is acquired as heat

heat

the process of transferring energy as a result of a temperature difference

work, heat

In molecular terms, _______ is the transfer of energy that makes use of organized motion of atoms in the surroundings and _______ is the transfer of energy that makes use of their disorderly motion

internal energy

the total energy of a system; is a state function. increases as the temperature is raised

equipartition theorem

can be used to estimate the contribution to the internal energy of each classically behaving mode of motion

First Law

states that the internal energy of an isolated system is constant

free expansion

expansion against zero pressure. does no work.

reversible change

a change that can be reversed by an infinitesimal change in a variable

reversible expansion

To achieve this, the external pressure is matched at every stage to the pressure of the system

energy transferred as heat, internal energy

The _______ at constant volume is equal to the change in _______ of the system

calorimetry

the measurement of heat transactions

enthalpy

energy transferred as heat at constant pressure is equal to the change in this of a system

heat capacity at constant pressure

equal to the slope of enthalpy with temperature

standard enthalpy of transition

equal to the energy transferred as heat at constant pressure in the transition under standard conditions

standard state

the pure form at 1 bar of a substance at a specified temperature

thermochemical equation

a chemical equation and its associated change in enthalpy

Hessâ€™s law

states that the standard reaction enthalpy is the sum of the values for the individual reactions into which the overall reaction may be divided

standard enthalpies of formation

these are defined in terms of the reference states of elements

reference state

most stable state at the specified temperature and 1 bar for an element

standard reaction enthalpy

the difference of the standard enthalpies of formation of products and reactants

Kirchhoffâ€™s law

the temperature dependence of a reaction enthalpy is expressed by this

internal pressure

the variation of internal energy with volume at constant temperature

Jouleâ€™s experiment

showed that the internal pressure of a perfect gas is zero

temperature, volume

the change in internal energy may be expressed in terms of changes in _______ and _______

Jouleâ€“Thomson effect

the change in temperature of a gas when it undergoes isenthalpic expansion

entropy

a signpost of spontaneous change: the entropy of the universe increases in a spontaneous process

entropy, reversible

A change in _______ is defined in terms of _______ heat transactions

Boltzmann formula

defines entropy in terms of the number of ways that the molecules can be arranged amongst the energy states, subject to the arrangements having the same overall energy

Carnot cycle

used to prove that entropy is a state function

efficiency

This of a heat engine is the basis of the definition of the thermodynamic temperature scale and one realization of such a scale, the Kelvin scale

Clausius inequality

used to show that the entropy of an isolated system increases in a spontaneous change and therefore that its definition is consistent with the Second Law

spontaneous, equilibrium

_______ processes are irreversible processes; processes accompanied by no change in entropy are at _______

entropy, isothermally

the _______ of a perfect gas increases when it expands _______

enthalpy of transition

the change in entropy of a substance accompanying a change of state at its transition temperature is calculated from its _______

heat capacity

the increase in entropy when a substance is heated is calculated from its _______

Nernst heat theorem

states that the entropy change accompanying any physical or chemical transformation approaches zero as the temperature approaches zero: Î”S â†’ 0 as T â†’ 0 provided all the substances involved are perfectly ordered

third Law of thermodynamics

states that the entropy of all perfect crystalline substances is zero at T = 0

residual entropy

the entropy arising from disorder that persists at T = 0 for a solid

third-law entropies

entropies based on S(0) = 0

standard entropies of ions in solution

based on setting S^â¦µ(H+, aq) = 0 at all temperatures

standard reaction entropy

Î”rS^â¦µ
the difference between the molar entropies of the pure, separated products and the pure, separated reactants, all substances being in their standard states

criteria for spontaneous change

The Clausius inequality implies a number of _______ under a variety of conditions which may be expressed in terms of the properties of the system alone; they are summarized by introducing the Helmholtz and Gibbs energies

spontaneous process

is accompanied by a decrease in the Helmholtz energy at constant temperature and volume. is accompanied by a decrease in the Gibbs energy at constant temperature and pressure

maximum work

The change in the Helmholtz energy, obtainable from a system at constant temperature

maximum non-expansion work

The change in the Gibbs energy, obtainable from a system at constant temperature and pressure

standard Gibbs energies of formation

used to calculate the standard Gibbs energies of reactions

fundamental equation

a combination of the First and Second Laws, is an expression for the change in internal energy that accompanies changes in the volume and entropy of a system

Maxwell relations

a series of relations between partial derivatives of thermodynamic properties based on criteria for changes in the properties being exact differentials

thermodynamic equation of state

The Maxwell relations are used to derive the _______ to determine how the internal energy of a substance varies with volume.

temperature, pressure

The Gibbs energy of a substance decreases with _______ and increases with _______

Gibbsâ€“Helmholtz equation

the variation of Gibbs energy with temperature is related to the enthalpy through this.

solids, liquids, gases

The Gibbs energies of _______ and _______ are almost independent of pressure; those of _______ vary linearly with the logarithm of the pressure

phase

a form of matter that is uniform throughout in chemical composition and physical state

phase transition

the spontaneous conversion of one phase into another

equilibrium

the thermodynamic analysis of phases is based on the fact that at _______, the chemical potential of a substance is the same throughout a sample

phase diagram

indicates the values of the pressure and temperature at which a particular phase is most stable, or is in equilibrium with other phases

phase rule

relates the number of variables that may be changed while the phases of a system remain in mutual equilibrium

decreases

The chemical potential of a substance _______ with increasing temperature in proportion to its molar entropy

increases

The chemical potential of a substance _______ with increasing pressure in proportion to its molar volume

increases

The vapour pressure of a condensed phase _______ when pressure is applied

Clapeyron equation

an exact expression for the slope of a phase boundary

Clausiusâ€“Clapeyron equation

an approximate expression for the boundary between a condensed phase and its vapour