A system of physical chemistry - Index of

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A system of physical chemistry - Index of

TO A SYSTEM OF PHYSICAL CHEMISTRY

by W, we can state that the number of molecules, the potential energy

of which lies between W and W + dW, is given by—

dn = constant x N x e~'^'l^'^ . dW.

We can integrate this to obtain the number n^ of molecules of a

perfect gas (in equilibrium in a field of force at a uniform temperature)

which possess potential energy W^ that is all values from zero up to Wj.

If the total number of molecules in the system be N, the expression

is «i = N(i - ^-V*^).

If we introduce the Avogadro constant No, i.e. the number of molecules

in one gram-molecule, the above expression becomes—

«i = N(i - ^-V^i/''^),

where R is the gas constant per gram-molecule.

It follows from this that the number of molecules which possess

potential energy between W^ and infinity is (i - n^) which is equal to

N^-Wj/ftT or Nf-NflWi/RT^

Distribution of Molecular Velocities and Temperature. —On the kinetic

theory it is to be expected that the temperature of a gas should

be expressible in purely mechanical terms. We are already familiar

with the concept that temperature is measured by the kinetic energy of

the molecules. In view of the distribution of velocities and therefore

of kinetic energy, among molecules, as expressed in Maxwell's law, it

is evident that the kinetic energy of a given individual molecule may be

very different from that possessed by another molecule of the same

system. Further, the kinetic energy of one and the same molecule

varies from moment to moment as a result of collisions. The temperature

of the system—measured in the ordinary way, by means of a thermometer—

is a perfectly definite quantity for the gas system as a whole

in the steady state. The temperature, in fact, is determined by the

average kinetic energy. It is therefore meaningless to speak of the

temperature of a single molecule in a gas. Temperature is essentially

a statistical effect due to the presence of a large number of molecules

each contributing its own share to the total effect. Two independent

systems are at the same temperature when the average kinetic energy

of each is the same. This is true whether the systems be gaseous,

liquid, or solid, homogeneous or heterogeneous.

It will be appreciated at the same time that pressure is likewise a

statistical effect. A single gas molecule cannot be conceived of as

exerting observable pressure, though each molecule exerts a certain

force against the walls of the containing vessel, the total effects of which,

when numerous molecules take part, is manifested as a uniform gas

pressure.

Entropy and Thermodynamic Probability.

It is proposed to indicate how the second law of thermodynamics

can be deduced on the basis of statistical mechanics. This was first

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