Kinetic Theory : Absolute Temperature

The product pv for a given weight of gas is proportional to the absolute temperature: pv = RT. But pv is proportional to the translational kinetic energy of the gas molecules, hence the latter is also proportional to the absolute temperature. Since, at constant volume, the pressure increases by 1/273 of its value at 0° C. for 1° rise in temperature, the translational kinetic energy of the molecules must increase by the same fraction of its value at 0° C. In this way we can easily calculate the molecular speeds at any temperature from their values at 0° C. given in the table in Molecular energy section.

Thus, the mean speed of hydrogen molecules at 1000° C. is found as follows: kinetic energy at 1000° = (1273/273) x K.E. at 0° C. But the speed is proportional to √(K.E.);

speed at 1000°/speed at 0° = √(1273) / √(273);

speed at 1000° = 1700 x √(1273/273) = 1700 x 2.16 m. per sec.

The increase of speed with temperature is therefore not very rapid; it is doubled by a rise of 1000°.

For a gram molecule, pv = RT. The kinetic energy of translation of the molecules is ½MG² = 3/2*pv = 3/2*RT. The value of R in absolute units is 8.317x10⁷ ergs per 1°, hence the translational kinetic energy at T° absolute is 3/2 x 8.317 x 10⁷ ergs = 12.476 x 10⁷ T ergs. In g. cal. it is 3/2 x 1.988 T = 2.982 T g. cal.

Protein crystallography
Chemistry guide
Kinetic Theory
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