Formulation of the First Law

The first law can be stated that the energy is not dependent on the path, in that we have reached certain parameters that characterize the energy. These parameters are in general the thermodynamic variables. This law can be stated also mathematically that the energy is a sole function of the thermodynamic variables themselves. In other words, we do not need other variables to ensure that the energy has just this value. Therefore, we may write the energy in the usual form  

This view is somehow an idealization, in contrast to common sense. For example, to bring a weight from sea level to a certain mountain, either with a cable car or on the road, the first law says that the same amount of energy is needed. This is against 

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The classical formulation of the first law of thermodynamics defines the change dU in the internal energy of a system as the sum of heat dq absorbed by the system plus the work dw done on the system ... 

Equation 10.1.1 represents a very general formulation of the first law of thermodynamics, which can be readily reduced to a variety of simple forms for specific applications under either steady-state or transient operating conditions. For steady-state applications the time derivative of the system energy is zero. This condition is that of greatest interest in the design of continuous flow reactors. Thus, at steady state,... 

On the theoretical side, it was Hermann von Helmholtz (Sidebar 3.4) who first presented a clear and comprehensive mathematical formulation of energy conservation as a principle of universal validity, applicable to all natural phenomena. Helmholtz s landmark paper of 1847, Uber die Erhaltung der Kraft, reflected some lingering ambiguities of the force (Kraft) concept, but exhibited the deep integration of the first law into analytical dynamics in a clear and modem way. Helmholtz deserves to be counted the scientist most responsible for rigorous mathematical formulation of the first law. 

Equation (6.2.9) represents the local formulation of the First Law of Thermodynamics when there is no motion of the center of mass. Note again that Eq. (6.2.7) and (6.2.9) are not averaged... 

Fig. 4.5. The two commonly used conventions for the sign of q and w, leading to two formulations of the First Law.

Thus, the work done by the system in an adiabatic process is independent of the path. This is an important experimental fact and was quite significant in the history of the formulation of the first law. 

In the preceding chapter we discussed the formulation of the first law of thermodynamics and some of its consequences. The first law defines a function of state, the energy, and restricts the region of conceivable processes to those in which the energy is conserved. In this chapter we shall formulate the second law of thermodynamics and develop some of its consequences. The second law defines a function of state, the entropy, and determines the direction in which possible processes will proceed in a given system. Those processes which are physically realizable are termed natural processes. 

In three variables, there are two additional analogous equations. Similar relations are valid also for other thermodynamic functions. The relation Eq. (1.28) is claimed to be the formulation of the first law of thermodynamics in the form of Jacobian determinants [9],... 

The incorporation of heat effects into the energy balance constitutes one of the fundamental principles of thermodynamics known as the first law. This chapter is devoted to the mathematical formulation of the first law and in the definition of two thermodynamic properties, internal energy and enthalpy, both of which are important in the calculation of energy balances. 

Similar to the mass conservation laws, the macroscopic formulation of the First Law of Thermodynamics—that is, energy is conserved—is applicable to a wide range of chemical processes and process elements. The energy conservation equation for a multicomponent mixture can be written in a bewildering array of equivalent forms. For the volume of qpace shown in Fig. 2.2-1 containing i species, one form of the conservation equation for the energy (internal + kinetic -I- potential) content of the system is... 

For the two special processes discussed above 5 W equals a perfect differential as shown by Eqs. (3.79) and (3.81). Expressing both SQ and SW exclusively by state variables makes (3.78) is a much more useful and generally valid formulation of the first law of thermodynamics. It must be noted that while da and ASy are perfect differentials by themselves, the products da and TyASy involving also dependent variables are trae differentials only in special cases, but not in general. 

This important empirical result has, of course, been confirmed by many later workers and using several substances other than water. Without discussing the great mass of evidence, we shall therefore make a preliminary formulation of the first law of thermodynamics as follows the change of a body inside an adiabatic enclosure from a given initial state to a given final state involves the same amount of work by whatever means the process is carried out.f... 

The mechanical view of nature holds that all energy is ultimately reducible to kinetic and potential energy of interacting particles. Thus, the law of conservation of energy may be thought of as essentially the law of conservation of the sum of kinetic and potential energies of all the constituent particles. Cornerstones for the formulation of the First Law are the decisive experiments of James Prescott Joule (1818-1889) of Manchester, a brewer and an amateur scientist. Here is how Joule expressed his view of conservation of energy [2, 3] ... 

There is another aspect of the formulation of the first law of thermodynamics expressed in Equation (2) that is almost completely counterintuitive. The term on the left-hand side, Af/, the change in internal energy of the system, depends only on the difference between the initial and final conditions. However, the amount of heat, Q, released or absorbed by the reaction and the amount of work done by the system depends upon the way the process is carried out. It is the difference between Q and W that depends only on the initial and final conditions. A detailed analysis of this important but rather obscure result is beyond the scope of our introductory discussion. 

With the technical development of the steam engine, this limitation of the motive power of heat was an urgent question in the beginning of the 1800s, i.e. before the formulation of the first law. In 1824, the French engineer Sadi Carnot presented his theory on the motive power of heat - this theory later formed the basis for the second law of thermodynamics, and for the definition of the concept of entropy. 

This energy reflects the total energy contained within a body, i.e. independently of its potential and kinetic energies, and is essential in the formulation of the first law of thermodynamics. (We shall return to this subject in Section 1.9.)... 

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