From Current Literature

On the Application of the Second Law of Thermodynamics to a Living Organism

Curt Wachtel. Über die Anwendbarkeit des zweiten Hauptsatzes der Thermodynamik auf Vorgänge im tierischen Organismus. Pflügers Archiv. Bd. 171. p. 66 (1918).

“An investigation of the applicability of the second law of thermodynamics to processes in the living organism seems superfluous to many, since the second law is a generally recognized law of nature and cannot be called into question. It should be pointed out, however, that the second law of thermodynamics is an empirical law whose applicability to the phenomena studied by physics is beyond doubt; conversely, not in a single case has it so far been possible to establish the applicability of the second law to phenomena in living organisms with the same degree of indisputability as is appropriate in the physical disciplines.” With these words the author begins his article, which presents a critical survey of the material available to physiologists on the applicability of thermodynamics to vital phenomena.

The author writes out the first and second laws of thermodynamics in their usual classical form and, on the basis of extensive material, studies chiefly the efficiency coefficient \(\left(k = \dfrac{A}{Q}\right)\), where \(k\) is the efficiency coefficient, \(A\) is the amount of work produced, and \(Q\) is the amount of heat thereby obtained.

The author gives several methods for calculating the efficiency coefficient.

First of all, Danilevsky, assuming that a worker can produce 7 kilogrammeters of work in the course of one second and that the working day is equal to 8 hours, finds the work for a day to be on average 200,000 kilogrammeters; during the same time the total consumption of energy by the organism is equal to 1,371,000 kilogrammeters. Taking the work of the heart and respiration to be 100,000 kilogrammeters, Danilevsky finds \(k = \dfrac{300{,}000}{1{,}371{,}000}\), i.e. about 22%. If one assumes results more suited to actual conditions, the coefficient \(k\) is smaller; and in general, depending on the kind of work, as later investigations showed, it ranges from 1% to 20%.

Next come the works of Chauveau, who made use of the formula

\[ D = A + Q_1 + Q_2, \]

where \(D\) is the total energy consumption, \(A\) is the work of the motor, \(Q_1\) is the energy supplied to the motor if it supports a load, and \(Q_2\) is the energy supplied to a motor running idle with a speed equal to that with which it moves while performing the work \(A\). Chauveau, however, was unable to verify his formula precisely on muscle, owing to the impossibility of expressing numerically all the terms of the formula, and in the best cases only an approximate value of \(D\) could be obtained.

Zuntz obtained the efficiency coefficient of the whole organism by studying, on the one hand, the metabolism during walking on level ground and, on the other, the metabolism during ascent, when a definite amount of work is performed. The increase in metabolism, expressed in calories, is, according to Zuntz, used for the work of ascent.

For excised frog muscles, Fick finds \(k = 25\%—30\%\). Bernstein, considering the work of a muscle as a consequence of capillary forces, finds \(k = 20\%\).

Of particular importance are the works of Baron and Polanyi, who proceeded in their calculations from definite reactions in the body of an animal and computed what work these reactions can yield; the authors assumed that the reaction proceeds at constant temperature and that, for example, grape sugar is converted into \(CO_2\) and \(H_2O\) according to the formula \(C_6H_{12}O_6 + 6O_2 = 6CO_2 + 6H_2O\) \((t = 37^\circ C)\). Similar schemes are given for proteins, fats, etc. “Quite convincing results for the applicability of the second principle, however, these experiments did not give,” as Wachtel also notes.

Summing up all that has been presented and taking into account that \(k\) fluctuates from \(1\%\) to \(30\%\), Wachtel comes to the fair conclusion that no quantitative confirmation exists for the applicability of the second principle of thermodynamics to vital phenomena, although all qualitative phenomena speak in favor of its applicability.

P. Lazarev.