General Exposition

Excerpts

• General Exposition

  *it is in no way possible, either by mechanical, thermal, chemical, or other devices, to obtain perpetual motion*, *i.e.* it is impossible to construct an engine which will work in a cycle and produce continuous work, or kinetic energy, from nothing.

• General Exposition

  The mechanical equivalent of the external effects is zero, or the external heat effect is equal in magnitude and opposite in sign to the external work.

• General Exposition

  The energy of the system in a given state, referred to the arbitrarily selected normal state, is then equal to *the algebraic sum of the mechanical equivalents of all the effects produced outside the system when it passes in any way from the given to the normal state*.

• General Exposition

  The only point of importance is that the state produced in the liquid by friction is identical with a state produced by the absorption of a definite number of calories.

• General Exposition

  That all his experiments with different weights, different calorimetric substances, and different temperatures, led to the same value, goes to prove the correctness of the principle of the conservation of energy.

• General Exposition

  The determination of the mechanical equivalent of heat enables us to express quantities of heat in ergs directly, instead of calories. The advantage of this is, that a quantity of heat is not only proportional to, but directly equal to its mechanical equivalent, whereby the mathematical expression for the energy is greatly simplified.

• General Exposition

  In the case of a gas which is being compressed by a weight sinking to a lower level, if the gas by itself be the system considered, the external effect on it is equal to the work done by the weight. The energy of the system accordingly increases. If, however, the weight and the earth be considered parts of the system, all external effects are eliminated, and the energy of this system remains constant.

• General Exposition

  Special care must be taken, however, that the initial state of the system is the same each time, and that none of the external effects is overlooked or taken into account more than once.

• General Exposition

  It will be different, however, in the case of the *second law* of thermodynamics, the proof of which, at the present stage of the development of our subject, cannot be too carefully presented. The general validity of this law is still contested from time to time, and its significance variously interpreted, even by the adherents of the principle.

• General Exposition

  Or we may, as is done in this work, leave open the question concerning the possibility of reducing all natural processes to those of motion, and start from the fact which has been tested by centuries of human experience, and repeatedly verified, viz. that *it is in no way possible, either by mechanical, thermal, chemical, or other devices, to obtain perpetual motion*, *i.e.* it is impossible to construct an engine which will work in a cycle and produce continuous work, or kinetic energy, from nothing.

Equations

• General Exposition

  U_{2} - U_{1} = Q + W\Add{.}

  The increase of the energy of a system undergoing a change equals the mechanical equivalent of the heat absorbed plus the work expended on it.

• General Exposition

  U_{2} = U_{1}

  For a cycle of operations, where the final state is the initial state, the energy of the system is the same at the end as at the start.

• General Exposition

  Q + W = 0\Add{.}

  For a cycle of operations the mechanical equivalent of the external heat effect equals in magnitude and opposite in sign the external work, so their sum is zero; this shows perpetual motion is impracticable.

• General Exposition

  U = \const

  If no external effects are produced by a change of state, the energy of the system remains constant.

• General Exposition

  U_{2} - U_{1} = U_{2}

  When state 1 is taken as the normal state, the energy of state 2 referred to it equals the difference U_2 - U_1, since U_1 is zero.

• General Exposition

  U_{1} = 0

  Taking state 1 as the normal state, its energy is zero, because no energy is needed to bring the system from state 1 to the normal state.

Problems

No exercises in this chapter.