Intrinsic energy

S-S annihilation phenomena can be considered as a powerful tool for investigating tire exciton dynamics in molecular complexes [26]. However, in systems where tliat is not tire objective it can be a complication one would prefer to avoid. To tliis end, a measure of suitably conservative excitation conditions is to have tire parameter a< )T < 0.01. Here x is tire effective rate of intrinsic energy dissipation in tire ensemble if tire excitation is by CW light, and T = IS tire... 

In principle, energy-analyzer systems can be designed such that their electron-optical properties do not limit the energy resolution attainable, i. e. their intrinsic energy resolution is much better than the energy width of the primary electron beam, which is of the order of approximately 1.5-2.5 eV for a tungsten hairpin cathode, approximately 1 eV for a LaBg cathode, approximately 0.7 eV for a Schottky field emitter, and 0.3-0.5 eV for a pure cold-field emitter. 

Definition of Intrinsic Energy.—Let there be given any system of bodies, and let the system undergo any change whatever, so that it passes from a given initial state [1] to a final state [2], the only condition imposed on the states [1] and [2] being that they shall be consistent with the physical properties of the system. 

Then if Ui be the intrinsic energy of the system in its initial state, and U2 the intrinsic energy of the system in its final state, we define the increase of intrinsic energy of the system by the equation ... 

An aschistic process implies constancy of intrinsic energy. 

The actual state, and absolute amount, of intrinsic energy existing in a body, or system of bodies, are things which lie quite outside the range of pure thermodynamics. This indefiniteness has, however, not the slightest influence on the stringency of the definition, since we can proceed as in the definition of electrostatic potential, and choose any convenient standard state of the body, and use the term intrinsic energy with reference to this standard state. 

If Uo is the absolute amount of intrinsic energy contained in a system (with reference to a state of absolute zero of energy) in an arbitrary standard state, and if in any change from a state [1] to a state [2] the total amounts of heat absorbed and work done are 2Q and 2A respectively, we have ... 

It will be observed that the definition of intrinsic energy by means of the equation (c) implies in itself no physical law, since the value of (U2—Ui) can always be chosen so as to make the values of 2Q and 2A satisfy the equation. We shall now show that the value of (U2 — Ui) is uniquely so defined, and is quite independent of the way in which the process is executed. This is a physical law, which we shall call the Principle of Conservation of Energy. 

The change of intrinsic energy of a system undergoing any change of state depends solely on the initial and final states of the system, and is independent of the manner in which the change from the one state to the other is effected. 

This very important theorem was recognised by R. Clausius in 1850, although he did not at the time give the very simple interpretation, in terms of the conception of intrinsic energy, which was brought forward by Lord Kelvin a year later. 

U = constant. The Principle of Conservation of Energy is usually expressed in the form that the intrinsic energy of an absolutely isolated system of bodies is constant and independent of all changes of state which may occur subject to the condition that the system remains isolated. Since in this case we have absolutely no means of examining the energy content of the system, the statement appears somewhat indefinite. 

The heat absorbed in the change of state of a system at constant volume is equal to the increase of intrinsic energy ... 

Corollary 2.—A body cooled to the zero of absolute temperature ( absolute zero ) cannot be made to part with more heat. [Its intrinsic energy may, however, have any value, including zero, at this temperature.]... 

This integral may therefore be regarded as measuring the change of some magnitude which depends, like the intrinsic energy, entirely on the actual state of a material system, and is independent of the previous history of the system. If SA, SB... 

Just as the intrinsic energy of a body is defined only up to an arbitrary constant, so also the entropy of the body cannot, from the considerations of pure thermodynamics, be specified in absolute amount. We therefore select any convenient arbitrary standard state a, in which the entropy is taken as zero, and estimate the entropy in another state /3 as follows The change of entropy being the same along all reversible paths linking the states a and /3, and equal to the difference of the entropies of the two states, we may imagine the process conducted in the following two steps ... 

As an example of a negative heat capacity we have the specific heat of saturated steam. If unit mass of steam in the condition of saturation is raised one degree in temperature, and at the same time compressed so as to keep it just saturated at each temperature, it is found that heat is evolved, not absorbed, because the work spent in the compression exceeds the increase of intrinsic energy. 

Let AU denote the change of intrinsic energy, and let Q be the amount of heat absorbed at the temperature T, in any part of the process. Then, according to the first law ... 

Let AU, AU + dAU be the amounts by which the intrinsic energy increases during the changes of configuration from the initial to the final state at the temperatures T and T + ST respectively, and let Tif 17 be the heat capacities at constant configuration of the initial and final states at the mean temperature T -J- ST. The sum of the changes of intrinsic energy in the four processes is then ... 

The change of intrinsic energy in an isothermal process increases... 

This shows that a part of the heat absorbed depends on the change of temperature, and another on the change of volume. The latter is composed of the external work pdv and a part depending on the change of intrinsic energy with volume. 

Show that p T = f(v) is the characteristic equation of a fluid the intrinsic energy of which is independent of the volume. 

Both conditions must be satisfied simultaneously, for the condition that both phases become identical at the critical point certainly requires that their intrinsic energies and entropies per unit mass are equal ... 

The entropy and intrinsic energy of steam (or other vapours) may be determined by the following method, due to Clausius. 

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