Internal energy and the first law

It will be remembered that an adiabatic wall was defined as one which prevents an enclosed body being influenced from beyond, except by the effect of motion. (We are not concerned here with force fields.) Experience shows that when there is motion of the wall, or parts of it, the state of the adiabatically enclosed body can be changed for example by compressing or expanding the enclosing wall, or by shaking the body inside. The first law of thermodynamics is based on a consideration of such processes which involve the performance of work..  

The first law is based mainly on the series of experiments carried out by Joule between 1843 and 1848. The most familiar of these experiments is the one in which he raised the temperature of a quantity of water, almost completely surrounded by an adiabatic wall, by means of a paddle which was operated by a falling weight. The result of this experiment was to show an almost exact proportionality between the amount of work expended on the water and the rise in its temperature. This result, considered on its own, is not very significant the really important feature of Joule s work was that the paddle-wheel experiments gave the same proportionality as was obtained in several other quite different methods of transforming work into the temperature rise of a quantity of water. These were as follows  

The figures in brackets show the number of foot-pounds of work needed to raise the temperature of 1 lb. of water by 1 °F. The result of the most accurate series of experiments, those with the paddles, is equivalent to 4.16joules/cal (15 °C), which is close to the present accept value of 4.184. However, the significant conclusion is that each of the four different methods of transforming work into a temperature rise gives essentially the same result— at any rate to within the accuracy which could be attained in these early experiments.  

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 

It will be recognized that statements similar to this are met with in other branches of physics. Thus the work required to lift a weight between two points in a gravitational field, or to move a charge between two points in an electric field, is the same whatever is the path. In both of these examples it is possible to define a potential function, such that the work done on a body in taking it from an initial state to a final state B is equal to / b — a where and depend only on the states A and B— i.e. they are independent of the path. 

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The Entropy and Irreversible Processes.—Unlike the internal energy and the first law of thermodynamics, the entropy and the second law are relatively unfamiliar. Like them, however, their best interpretation comes from the atomic point of view, as carried out in statistical mechanics. For this reason, we shall start with a qualitative description of the nature of the entropy, rather than with quantitative definitions and methods of measurement. 

Consider next the energy equation, neglecting kinetic and gravitational-potential energy. Here the extensive variable is the internal energy of the gas E and the intensive variable is the specific internal energy e. The first law of thermodynamics provides the system energy balance... 

Because the unit of electric potential is V and the unit of charge is C, equation 8.7 shows that the unit for work using equation 8.8 is joules. Now that we are considering a new kind of work, we must remember to include this as part of the total change in internal energy under the first law of thermodynamics. That is, the infinitesimal change in the internal energy is now... 

It has been seen thus far that the first law, when applied to thermodynamic processes, identifies the existence of a property called the internal energy. It may in other words be stated that analysis of the first law leads to the definition of a derived property known as internal energy. Similarly, the second law, when applied to such processes, leads to the definition of a new property, known as the entropy. Here again it may in other words be said that analysis of the second law leads to the definition of another derived property, the entropy. If the first law is said to be the law of internal energy, then the second law may be called the law of entropy. The three Es, namely energy, equilibrium and entropy, are centrally important in the study of thermodynamics. It is sometimes stated that classical thermodynamics is dominated by the second law. 

Suppose any closed system (thus having a constant mass) undergoes a process by which it passes from an initial state to a final state. If the only interaction with its surroundings is in the form of transfers of heat, Q, and work, W, then only the internal energy, U, can be changed, and the First Law of Thermodynamics is expressed mathematically as... 

In addition, the First Law of Thermodynamics states that the change in internal energy and the work done in expansion are driven by the total heat input according to the equation ... 

As a statement of energy conservation, the first law is the starting point for all energy balances in a closed system. Problems of this type typically require the calculation of heat and work. The amount of heat that is exchanged can, under special conditions, be related to internal energy or enthalpy ... 

The zone fire models discussed here take the mathematical form of an initial value problem for a system of differential equations. These equations are derived using the conservation of mass or continuily equation, the conservation of energy or the first law of thermodynamics, the ideal gas law, and definitions of density and internal eneigy. The conservation of momentum is ignored. These conservation laws are invoked for each zone or control volume. A zone may consist of a number of interior regions (usually an upper and a lower gas layer), and a number of wall segments. The basic assumption of a zone fire model is that properties such as temperatures can be uniformly approximated throughout the zone. It is remarkable that this assumption seems to hold for as few as two gas layers. 

Although the internal energy represents the total energy of a system, and the first law of thermodynamics is based on the concept of internal energy, it is not always the best variable to work with. Equation 2.15 shows that the change in the internal energy is exactly equal to q—if the volume of the system remains constant for a particular process. However, not all processes occur at constant volume. In fact, constant pressure processes, in which the system is exposed to the atmosphere, are more common. Enthalpy is given the symbol H. The fundamental definition of enthalpy is... 

The structure of this text is kept simple in order to make the succession of steps as transparent as possible. The first chapter Two Fundamental Laws of Nature) explains how the first and the second law of thermodynamics can be cast into a useful mathematical form. It also explains different types of work as well as concepts like temperature and entropy. The final result is the differential entropy change expressed through differential changes in internal energy and the various types of work. This is a fundamental relation throughout equilibrium as well as nonequilibrium thermodynamics. The second chapter Thermodynamic Functions),... 

The form of Equation (5.4) is general and we can use it to express any of the properties we examined in Section 5.1 in terms of two independent properties. For example, say we want to calculate the change in internal energy for a first-law analysis of a closed system. We may choose to relate the differential change in internal energy, dit, to the measured properties temperature, T, and molar volume, v. In the form of Equation (5.4), we write ... 

In the same way that the first law of thermodynamics cannot be formulated without the prior recognition of internal energy as a property, so also the second law can have no complete and quantitative expression without a prior assertion of the existence of entropy as a property. 

The fundamental thermodynamic properties that arise in connection with the first and second laws of thermodyuamics are internal energy and entropy These properties, together with the two laws for which they are essential, apply to all types of systems. However, different types of systems are characterized by different sets of measurable coordinates or variables. The type of system most commonly... 

It follows directly from the first law of thermodynamics that if a quantity of heat Q is absorbed by a body then part of that heat will do work W and part will be aecounted for by a rise in the internal energy AE of that body, i.e. 

The first law of thermodynamics states that the internal energy of an isolated system is constant. A state function depends only on the current state of a system. The change in a state function between two states is independent of the path between them. Internal energy is a state function work and heat are not. 

Based on the law of conservation of energy, energy balances are a statement of the first law of thermodynamics. The internal energy depends, not only on temperature, but also on the mass of the system and its composition. For that reason, mass balances are almost always a necessary part of energy balancing. 

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