Cases in which the equality sign holds are ideal cases only; but they are approximated to more nearly the nearer a system keeps in equilibrium states throughout.
The quantity is, as we have said, the absolute temperature according to a perfect gas scale. We could have defined it alter natively in terms of the efficiency equation and it is therefore called the thermodynamic temperature. It would have been nec essary then to show that it is identical with the ideal gas scale.
The advantage gained by introducing the conception of entropy is that it provides us with a function of Q which depends (unlike Q itself) only upon the state of the system, provided that we meas ure it for reversible changes only.
viii. When any property of the state of a system (say E) is defined completely by two independent variables (say x and y) so that we can write the suffixes denoting quantities which remain constant during the partial differentiations to which they are appended.
This mathematical relation can be applied in the case of re versible changes to E and 4) which depend only on the state but it cannot be applied to Q or to IV, which depend upon the path taken between the extreme states. In consequence some writers prefer not to use the expressions dQ and diV for small changes in Q and W because, for example, these may each acquire dif ferent values whether the "co-ordinates" of the system (e.g.,
The thermodynamic equations employed above are exact. It should be noted, however, that the characteristic equations are only approximate at best. The underlying assumption that is made in deriving them is that the system consists of molecules alike in all respects. Even in such a case it is not to be expected that the p, v, T, equation should be of a simple form. It is much simplified by the fact that we are only concerned with average values. No instrument is capable of measuring either the pres sure or temperature at a single point and a single moment of time. Each quantity measured is an average value over such a volume or area or time as to maintain a constant value in the equilibrium state. For real fluids molecules may be of different kinds and may be associated with one another in different ways which change with the volume and temperature. In such cases the connection between v and T is bound to be of a more elaborate character. The only assumption that has been made is that for a definite p, v, T, the constitution is the same whenever these return, after changes, to their original values.