THERMODYNAMICS AND PHYSICAL CHEMISTRY Introductory.—The principles of thermodynamics (intro duced in their modern form by Clausius in i85o) are the basis of a method of dealing with mechanical problems in which heat exchanges take place, without the necessity arising of considering the detailed mechanical structure of a system. The system may consist of an assemblage of an enormous number of molecules in agitated movement and exerting attractions and repulsions upon one another. Very little can be found out about the individual motions and positions of these particles. Thermodynamics pro vides a means of examining certain properties of matter in bulk. The principles that are discovered form the basis of the preceding article and reference must be made to that article for their de scription and proof. They are applied there mainly to the prop erties of steam and its applications to steam-engines. In the pres ent article which deals with the application to bodies in general we must be content with summarizing the fundamental facts which will be utilized.
i. The intrinsic or internal energy of a body can change by the entry of heat (by conduction or radiation) and by the per formance of external work, i.e., dE=dQ—dW provided the sys tem remains sensibly in equilibrium (Conservation of energy).
ii. A body may get hotter even if no heat flows in. The energy depends on the temperature and this is increased if work is done upon the system even when dQ is zero (Adiabatic changes).
iii. The energy, E, depends only upon the state; so that, in whatever way the system is changed, if the original state is re turned to the initial value, E, is recovered.
iv. The work done depends in general not only upon the ini tial and final states but also upon the path of transformation.
This results from the fact that three variables at least are nec essary to specify the state, viz., pressure, volume and tempera ture, and they are connected by only one equation (the equation of state). The work done is in each case f pdv . In a complete cycle the work done is equal to the area enclosed by the cycle on a p, V diagram. For any given value of V ,T and therefore p may have different values on the return and forward paths and the cycle encloses an area. It follows that for an isothermal reversible cycle the pressure for any given volume is fixed and the work done must be zero for the path then returns on itself.
v. The energy E depends on both the temperature and the volume: for internal work can be done against molecular attrac tions when the volume changes.
When the system is subjected to a uniform pressure the funda mental equation becomes dH=CdT+ldv.
We select unit mass for consideration. In this case C is the vi. The second law of thermodynamics enables relations to be found between the several quantities (or their derived quan tities). According to this law the work that can be done in a reversible Carnot cycle is the maximum possible for the two ex treme temperatures concerned, and, independently of the working substance, the work done divided by the heat taken in at the higher temperature is equal to ( T2)/Ti: where T1 and T2 are absolute temperatures on the perfect gas scale. This ratio is called the efficiency.
[This law is derived from the fact that heat can only flow down a gradient of temperature. Clausius showed that if a more effi cient performance were obtainable it would be possible to make a hot body hotter while simultaneously a cold one became colder without any performance of work. This would entail that heat flowed up the temperature gradient.] Now in a Carnot cycle and Q2 are the only transfers of heat (each at constant temperature) ; if therefore we define a quantity 4) such that Tcl4)=dQ this quantity 4) undergoes zero change in any complete reversible cycle. It is called the entropy of the sys tem per unit mass.
For irreversible changes this definition is not complete. In such changes there is kinetic energy of matter in bulk; and fric tion which is always present is continually frittering the motion down into heat. If we regard the system as an assemblage of small elements rubbing against one another the heat produced flows across the boundaries of these elements. In doing so some has entered each element and produces the same changes of p, v, T and entropy as any heat entry would do. When this heat pro duction and corresponding entropy change is summed up for the whole system we have Td4= d(Q+q) where q is the heat produced by friction inside the walls of the complete system. Since friction never produces "cold," dq is al ways positive and consequently for any change .Tcic/dQ.