His first contributions to mathematical physics were two papers published in 1873 in the Transactions of the Connecticut Academy on "Graphical Methods in the Thermodynamics of Fluids," and "Method of Geometrical Representation of the Thermodynamic Properties of Substances by means of Surfaces."
We may conclude that in polymorphs the substance occurs in different phases (or molecular aggregations), and the equilibrium between these phases follows definite laws, being dependent upon temperature and pressure, and amenable to thermodynamic treatment (cf.
Kohlrausch has prepared water of which the conductivity compared with that of mercury was only o 4 oX 11 at 18° C. Even here some little impurity was present, and the conductivity of chemically pure water was estimated by thermodynamic reasoning as o 36X1011 at 18° C. As we shall see later, the conductivity of very dilute salt solutions is proportional to the concentration, so that it is probable that, in most cases, practically all the current is carried by the salt.
This equilibrium pressure is called the osmotic pressure of the solution, and thermodynamic theory shows that, in an ideal case of perfect separation between solvent and solute, it should have the same value as the pressure which a number of molecules equal to the number of solute molecules in the solution would exert if they could exist as a gas in a space equal to the volume of the solution, provided that the space was large enough (i.e.
Thermodynamic theory also indicates a connexion between the osmotic pressure of a solution and the depression of its freezing point and its vapour pressure compared with those of the pure solvent.
(2) As the concentration of the solutions increases, the ionization as measured electrically and the dissociation as measured osmotically might decrease more or less together, though, since the thermodynamic theory only holds when the solution is so dilute that the dissolved particles are beyond each other's sphere of action, there is much doubt whether this second relation is valid through any appreciable range of concentration.
The second relation, as we have seen, is not a strict consequence of theory, and experiments to examine it must be treated as an investigation of the limits within which solutions are dilute within the thermodynamic sense of the word, rather than as a test of the soundness of the theory.
The forces between the ions of a strongly dissociated solution will thus be considerable at a dilution which makes forces between undissociated molecules quite insensible, and at the concentrations necessary to test Ostwald's formula an electrolyte will be far from dilute in the thermodynamic sense of the term, which implies no appreciable intermolecular or interionic forces.
Hence we get the equation Ee = Le +Te (dE/dT) or E = L+T(dE/dT), as a particular case of the general thermodynamic equation of available energy.
Any reversible cell can theoretically be employed as an accumulator, though, in practice, conditions of general convenience are more sought after than thermodynamic efficiency.
The fact that the Gibbs-Helmholtz equation is found to apply also indicates that the lead accumulator is approximately reversible in the thermodynamic sense of the term.
An ideal gas is a substance possessing very simple thermodynamic properties to which actual gases and vapours appear to approximate indefinitely at low pressures and high temperatures.
This function is also called the " thermodynamic potential at constant volume " from the analogy with the condition of minimum potential energy as the criterion of stable equilibrium in statics.
The condition of stable equilibrium is that G should be a minimum, for which reason it has been called the " thermodynamic potential at constant pressure."
The simplest application of the thermodynamic potential is to questions of change of state.
Writing formulae (3r) and (33) for the energy and entropy with indeterminate constants A and B, instead of taking them between limits, we obtain the following expressions for the thermodynamic functions in the case of the vapour: " =Solog e 0 - R log e p - ncp/D+A".
Although the value of G in any case cannot be found without that of 0, and although the consideration of the properties of the thermodynamic potential cannot in any case lead to results which are not directly deducible from the two fundamental laws, it affords a convenient method of formal expression in abstract thermodynamics for the condition of equilibrium between different phases, or the criterion of the possibility of a transformation.
A more common method of procedure, however, is to infer the general relations of the thermodynamic potential from a consideration of the phenomena of equilibrium.
0, Thermodynamic or absolute temperature.
G, J, Thermodynamic potential functions.
A saturated solution is a system in equilibrium, and exhibits the thermodynamic relations which hold for all such systems. Just as two electrified bodies are in equilibrium when their electric potentials are equal, so two parts of a chemical and physical system are in equilibrium when there is equality between the chemical potentials of each component present in the two parts.
By imagining that a dilute solution is put through a thermodynamic cycle we may deduce directly relations between its osmotic pressure and its freezing point.
When the solution ceases to be dilute in the thermodynamic sense of the word, that is, when the spheres of influence of the solute particles intersect each other, this reasoning ceases to apply, and the resulting modification of the gas laws as applied to solutions becomes a matter for further investigation, theoretical or experimental.
Such, a concordance between theory and experiment not only verifies the accuracy of thermodynamic reasoning as applied to dilute solutions, but gives perhaps one of the most convincing experimental verifications of the general validity of thermodynamic theory which we possess.
They merely show that, in the conditions of the particular experiments, the thermodynamic equilibrium value of the osmotic pressure cannot be reached - the thermodynamic or theoretical osmotic pressure (which must be independent of the nature of the membrane provided it is truly semi-permeable) is a different thing from the equilibrium pressure actually reached in a given experiment, which measures the balance of ingress and egress of solvent through an imperfect semi-permeable membrane.
The conceptions of osmotic pressure and ideal semi-permeable membranes enable us to deduce other thermodynamic relations between the different properties of solutions.
It follows that if the thermodynamic heat of solution be positive, that is, if heat be absorbed to keep the system at constant temperature, the solubility will increase with rising temperature, while if heat be evolved on dissolution, the solubility falls when the system is heated.
Whatever view, if any, be adopted as to the nature of a solution, the thermodynamic relations we have investigated equally hold good.
It is the strength and weakness of thermodynamic methods that they are independent of theories of constitution.
All the thermodynamic relations we have deduced hold on any theory of solution and favour no one theory rather than another.
But for any theory of solution to be tenable, it must at least be consistent with the known thermodynamic relations, verified as those relations are by experiment.
Thus prismatic sulphur has a higher melting-point (120°) than the rhombic form (116°), and it is even possible to calculate the difference theoretically from the thermodynamic relations.
The highest thermodynamic efficiency will be reached when the working substance is at the top of its temperature range while any heat is being received and at the bottom while any heat is being rejected - as is the case in the cycle of operations of the theoretically imagined engine of Carnot.
The stages at which heat is taken from the furnace and rejected to the cooler (C) are approximately isothermal at the upper and lower limits of temperature respectively, and the cycle accordingly is approximately "perfect" in the thermodynamic sense.
0, Temperature on thermodynamic scale.