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

**system**s are at the same temperature when the average kinetic energy

**of** each is the same. This is true whether the **system**s 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