The Elements of Electro-Chemistry

This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1896 Excerpt: ...is pdv, and the total work is p I dv, vj that is, p times the sum of these infinitely small amounts dv, from the value v to that of v, consequently = p(vl--v). Attention is here called to the introduction, p. 5, where it is shown that the-product pv, therefore p (wt--v) = pv2, represents a quantity of work. In the case under consideration the relations are not quite so simple, the pressure not remaining constant, but changing on the other hand with change of volume, until it reaches p. It is not enough then merely to add together the values dv; the sum of the endless number of infinitely small amounts of work pdv must be known, where the value of p is not a constant but a function of v, that is, in this case always possessing a value dependent upon that of the corresponding v. It may be expressed The values p and v are dependent upon each other in a definite and known manner. For molecular quantities we obtain from the gas-equation pv = RT, p = RT--. Substituting this value of p in the above v equation and placing the constants before the sign of summation (the integral sign), we get There is here only one variable, and the integral is determinable. We know that where In signifies the natural and log the ordinary logarithms; consequently v 0-4343 s v Since--=-1 according to the Boyle-Mariotte law, we have p1 0-4343 Pl A graphical method1 may be advantageously employed to make the calculation simpler to those who find difficulty in understanding the above expressions of higher mathematics. In a rectangular co-ordinate system measuring values of p on the axis of ordinates and v on the axis of abscissae, and using the values of p and v obtained from the gas-equation pv = RT as applied to a given gas, we obtain a curve as shown, which is a right-angled hyperbol...