# Eight Lectures on Theoretical Physics; Delivered at Columbia University in 1909 Volume 6

## Max Planck

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This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1915 edition. Excerpt: ...place of the three velocities WI, p2, p3, as the determining coordinates of the state. These are defined in the following way: wherein II denotes the kinetic potential (Helmholz). Then, in Hamiltonian form, the equations of motion are: . d+x (PEI dVl fdE (E is the energy), and from these equations follows the "condition of incompressibility " 1 + +... =0 dpi dpi Referring to the six-dimensional space represented by the coordinates pi, (2, pa, \$i, Tp2, \$3, this equation states that the magnitude of an arbitrarily chosen state domain, viz.: J' dpi. df2. dfz. dipi. dtyz. Ah, does not change with the time, when each point of the domain changes its position in accordance with the laws of motion of material points. Accordingly, it is made possible to take the magnitude of this domain as a direct measure for the probability that the state point falls within the domain. From the last expression, which can be easily generalized for the case of an arbitrary number of variables, we shall calulate later the probability of a thermodynamic state, for the case of radiant energy as well as that for material substances. FOURTH LECTURE. The Equation Of State for A Monatomic Gas. My problem today is to utilize the general fundamental laws concerning the concept of irreversibility, which we established in the lecture of yesterday, in the solution of a definite problem: the calculation of the entropy of an ideal monatomic gas in a given state, and the derivation of all its thermodynamic properties. The way in which we have to proceed is prescribed for us by the general definition of entropy: S = k log W. (13) The chief part of our problem is the calculation of W for a given state of the gas, and in this connection there is first required a more...

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