ties of the thermometric fluids constant, independent of temperature. Joule and Lord Kelvin2, in 1854,.proposed the particular thermodynamic scale now in use because it corresponds very closely to the mercury-inglass and gas thermometer scales in use as standards in 1854. This facilitated the adoption of the proposed scientific scale based on the laws of thermodGmics. On the thermodynamic scales mnu in use the expansivities of many substances are approximately constant. In general, this would not be true of other thermodynamic scales. F. G . BRICKWEDDE NATIONAL BUREAU OF STANDARDS D. C. WASHINGTON,
T o the Editor: In the September, 1940, issue of the JOURNAL in an article, "Upper Limit of Temperature," the equation T = 10-'/25 MuZis used in order to determine the highest possible temperature. This equation assumes a constant mass. ~ u1,orentz t has showti that as the velocity of lirht is aooroached. mass is meatlv,increased. until it .* becomes infinite a t the velocity of light itself. The equation given by Lorentz: 0
M =
m
-
41
-
$
where o is the velocity of light, m is mass a t rest, and M is mass a t velocity u, when combined with the first equation gives us a new equation: T
-
mu'
where u is velocity in cm./sec., m is the mass at rest, and 3 X 101° is the velocity of light in cm./sec. If the value u is equal to the velocity of light, the temperature becomes infinite. If u &r the hydrogen atom is 2.9 an./sec. the temperature 1s above degrees Kelvin as compared to the upper limit calculated in the article of 3.58 X 1012degrees Kelvin. However, these temperatures are excessive because the hydrogen atom will have ceased to exist at a temperature much lower than this, due to the complete conversion of the mass of the atom into radiant energy. This will be brought about by the radiations of short wave length which characteristically accompany high temperatures, as set forth in the relationship: wave length X temperature = 0.2885
The wave length short enough to cause the complete conversion of the hydrogen atom into radiant energy is equal to the wave length of the newly created radiation. By combining the four relationships:
1{
energy of quantum of radiation promass of hydrogen duced by complete conversion of = atom X (velocity of light)' hydrogen atom into radiant energy Planck's constant X frequency = energy of quantum
speed of light = frequency x wave length temperature x wave length = 0.2885 We
the equation: T =
0.2885 mu -
h
where T is the temperature in degrees Kelvin, m the mass of the hydrogen atom in grams (1.666 X v is the velocity of light in cm./sec. (3 X lolo), and h is Planck's constant (6.5 X 10F2'). In solving we find T to be 2.2 X 1012 degrees Kelvin. At this temperature the accompanying radiation will have a wave length short enough (1.3 X 10-lJ cm.) to cause the complete conversion of the mass of the hvdroeen . atom in& radiant energy and the temperature is therefore the highest temperature which the hydrogen atom can reach without being annihilated. WILLIAM COPULSKY
-
~,","~~y~~B","~~ T o the FAltor. F. G. Brickwedde correctly brings out in his interesting discussion of temperature scales that we cannot properly speak of an upper or lower limit of temperature. However, this does not preclude the possibility of limiting temperature states for a material body. The lowest l i t which a body can approach has been considered to be 273.16"C. However, no evidence seems to have been offered for a temperature state above which material bodies cannot exist. In order to stimulate discussion on this-point, I wrote "Upper Limit of Tergperature" (more properly. . .upper limit of temperature for the hydrogen atom on the Kelvin scale). In'the calculations, I assumed that a mass did not change with increasing velocity and that all the heat energy was transformed into .kinetic energy. This was obviously necessary to solv& the equation T = 10-'/25 Mu2. (The Lorentz formula is a theory. A widely accepted one, true, but no rigorous laboratory experiments have been made which eliminate the possibility of producing or assuming a system in which mass is kept constant with increasing velocity.) It is interesting to note tlfat WilIiam Copulsky does not make the assumption of a constant mass. From a consideration of the conversion of mass into radiant energy, he arrives a t the temperature of 2.2 X 10120K. his-is in substantial agreement with the temperature of 3.58 X 10120K. The highest temperatures recorded from measurements of heavenly bodies are from 4 to 5 X lo'. The highest temperature which a body can approach under ideal conditions is obviously somewhat higher. So far calculations indicate that it is in the neighborhood of 10120K. CARLROSENBLUM OLDTOWN RIBBONAND C A ~ OCO~PANY, N INC. BROORI-YN, NEWYORK
