Law of thermodynamics second

The second law of thermodynamics states that it is impossible to have an engine with a cycle that produces work while exchanging heat with a single reservoir. Another statement is that heat will not transfer from a cooler body to a warmer one without work being added. When heat is added to a body the mean amplitude of vibration of its molecules increases as its degree of structural order decreases. The maximum amplitude of vibration of the molecules in a body cannot be reduced without work being done on the body. 

We emphasize that the formulation according to Eq. (3.8) does not guarantee that the function U is not independent of its path. Conversely, from the value of the state function, we cannot conclude on the values of its arguments. 

Example 3.1. Academic teachers often stress the term state function. But most of them cannot exemplify any process that is not a state function. Here we show one example, the ideal gas 

We go first from room temperature T 0 and ordinary pressure p 0 to zero pressure p 0 and then to zero temperature r - 0 

Then we go from room temperature and ordinary pressure to zero temperature and 

Observe the difference. For an ideal gas, the zero temperature and the zero pressure are a singular point.  

In classical thermodynamics, the Second Law consists of two parts (see Kestin 1979). The first part defines the entropy for reversible processes based on Carathdodory s theorem. The latter part concludes that entropy increases in all irreversible processes. Recall that, as discussed in Sect. 3.1, the terminologies of the reversible and irreversible processes are used here in the sense of classical thermodynamics however, in this Section irreversible processes acquire a different interpretation to that used in the classical sense. That is, we may be able to introduce an apparent irreversible process for the case that considers a non-measurable energy, which will be discussed in more detail in Sect. 3.3.2. 

First we need to show the existence of entropy based on the auxiliary conservation of energy law (3.50). We will then indicate that irreversible processes, in the sense of the present work, result in an observational problem with any non-measurable data. 

Be familiar with the concepts of the first and second laws of thermodynamics. 

Be able to calculate free energies from equilibrium constants and redox potentials and do so under nonstandard conditions using the appropriate equations involving reactant and product concentrations at the beginning of the reaction. 

From free energy and redox potential calculations, be able to predict in which direction chemical reactions will proceed. 

Know the effect of temperature on equilibrium constants, free energy, and entropy and enthalpy changes. 

Be familiar with the concept of a high-energy phosphate bond, and be able to calculate the overall free energy change for reactions coupled to ATP hydrolysis. 

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In Section XVII-16C there is mention of S-shaped isotherms being obtained. That is, as pressure increased, the amount adsorbed increased, then decreased, then increased again. If this is equilibrium behavior, explain whether a violation of the second law of thermodynamics is implied. A sketch of such an isotherm is shown for nitrogen adsorbed on a microporous carbon (see Ref. 226). 

The Boltzmann distribution is fundamental to statistical mechanics. The Boltzmann distribution is derived by maximising the entropy of the system (in accordance with the second law of thermodynamics) subject to the constraints on the system. Let us consider a system containing N particles (atoms or molecules) such that the energy levels of the... 

The Carnot cycle is formulated directly from the second law of thermodynamics. It is a perfectly reversible, adiabatic cycle consisting of two constant entropy processes and two constant temperature processes. It defines the ultimate efficiency for any process operating between two temperatures. The coefficient of performance (COP) of the reverse Carnot cycle (refrigerator) is expressed as... 

Second Law of Thermodynamics. The entropy change of any system together with its surroundings is positive for a real process, approaching zero as the process approaches reversibiUty ... 

The foUowiag criterion of phase equUibrium can be developed from the first and second laws of thermodynamics the equUibrium state for a closed multiphase system of constant, uniform temperature and pressure is the state for which the total Gibbs energy is a minimum, whence... 

Under isothermal conditions where energy is not added or removed from the system, the second law of thermodynamics obtains, and... 

On purely kinetic grounds, however, the term random must be used carefully in describing a MaxweUian gas. The probabUity of a MaxweUian gas entering a duct is not a random function. This probabUity is proportional to the cosine of the angle between the molecular trajectory and the normal to the entrance plane of the duct. The latter assumption is consistent with the second law of thermodynamics, whereas assuming a random distribution entry is not. 

The second law of thermodynamics focuses on the quaUty, or value, of energy. The measure of quaUty is the fraction of a given quantity of energy that can be converted to work. What is valued in energy purchased is the abiUty to do work. Electricity, for example, can be totally converted to work, whereas only a small fraction of the heat rejected to a cooling tower can make this transition. As a result, electricity is a much more valuable and more costly commodity. 

Fundamental Property Relation. The fundamental property relation, which embodies the first and second laws of thermodynamics, can be expressed as a semiempifical equation containing physical parameters and one or more constants of integration. AH of these may be adjusted to fit experimental data. The Clausius-Clapeyron equation is an example of this type of relation (1—3). 

Funda.menta.1 PropertyRela.tion. For homogeneous, single-phase systems the fundamental property relation (3), is a combination of the first and second laws of thermodynamics that may be written as... 

Macroscopic and Microscopic Balances Three postulates, regarded as laws of physics, are fundamental in fluid mechanics. These are conservation of mass, conservation of momentum, and con-servation of energy. In addition, two other postulates, conservation of moment of momentum (angular momentum) and the entropy inequality (second law of thermodynamics) have occasional use. The conservation principles may be applied either to material systems or to control volumes in space. Most often, control volumes are used. The control volumes may be either of finite or differential size, resulting in either algebraic or differential consei vation equations, respectively. These are often called macroscopic and microscopic balance equations. 

As pointed out in Section 2.4, shock waves are such rapid processes that there is no time for heat to flow into the system from the surroundings they are considered to be adiabatic. By the second law of thermodynamics, the quantity (S — Sg) must be positive for any thermodynamic process in an isolated system. According to (2.54), this quantity can only be positive if the P-V isentrope is concave upward. Thus, the thermodynamic stability condition for a shock wave is... 

A thermodynamic change can take place in two ways - either reversibly, or irreversibly. In a reversible change, all the processes take place as efficiently as the second law of thermodynamics will allow them to. In this case the second law tells us that... 

The second law of thermodynamics was actually postulated by Carnot prior to the development of the first law. The original statements made concerning the second law were negative—they said what would not happen. The second law states that heat will not flow, in itself, from cold to hot. While no mathematical relationships come directly from the second law, a set of equations can be developed by adding a few assumptions for use in compressor analysis. For a reversible process, entropy, s, can be defined in differential form as... 

This expression insures that the heat-transfer considerations of the second law of thermodynamics are satisfied. For a given pair of corresponding temperatures (T, t) it is thermodynamically and practically feasible to transfer heat from any hot stream whose temperature is greater than or equal to T to any cold stream whose temperature is less than or equal to t. It is worth noting the analogy between Eqs. (9.2) and (3.5). Thermal equilibrium is a special case of mass-exchange equilibrium with T,t and AT " corresponding to yi,Xj and ej, respectively, while the values of rrij and bj arc one and zero, respectively. 

The second law of thermodynamics may be used to show that a cyclic heat power plant (or cyclic heat engine) achieves maximum efficiency by operating on a reversible cycle called the Carnot cycle for a given (maximum) temperature of supply (T ax) and given (minimum) temperature of heat rejection (T jn). Such a Carnot power plant receives all its heat (Qq) at the maximum temperature (i.e. Tq = and rejects all its heat (Q ) at the minimum temperature (i.e. 7 = 7, in) the other processes are reversible and adiabatic and therefore isentropic (see the temperature-entropy diagram of Fig. 1.8). Its thermal efficiency is... 

Since these were preliminary conclusions, further explanations of the.se disadvantages are given using the second law of thermodynamics in this chapter. The ideas of reversibility, irreversibility, and the thermodynamic properties steady-flow availability and exergy are also developed. 

In this chapter we will develop more rigorous approaches to the analysis of gas turbine plants using both the first and second laws of thermodynamics. 

The second law of thermodynamics has been described and expressed in many... 

According to the second law of thermodynamics, for a reaction to proceed spontaneously it must produce an increase in entropy (AS > 0). Because most spontaneous chemical reactions in the body are exothermic (AH < 0), most spontaneous chemical reactions will have AG values less than zero as well. This means that if, in the reaction shown in Equation... 

Carnot s research also made a major contribution to the second law of thermodynamics. Since the maximum efficiency of a Carnot engine is given by 1 -T( H, if the engine is to be 100 percent efficient (i.e., Cma = 1), Tc must equal zero. This led William Thomson (Lord Kelvin) to propose in 1848 that Tf must be the absolute zero of the temperature scale later known as the absolute scale or Kelvin scale. ... 

Because Carnot s 1824 manuscript remained unpublished at the time of his death m 1832, it was left to Kelvin and Rudolf Clausius to show how the second law of thermodynamics was implicit in Carnot s work. For this reason Kelvin once referred to Carnot as the profoundest thinker in thermodynamic philosopihy in the first thirty years of the nineteenth century. ... 

Mendoza, E., ed. (1960). Reflections on the Motive Power of Fire by Sadi Carnot and Other Papers on the Second Law of Thermodynamics by E. Clapeyron and R. Clausius. New York Dover Publications, Inc. 

In his first work on thermodynamics in 1873, Gibbs immediately combined the differential forms of the first and second laws of thermodynamics for the reversible processes of a system to obtain a single Tundamciital equation ... 

The second law of thermodynamics further restricts the types of processes that are possible in nature. The second law is particularly important in discussions of energy since it contains the theoretical limiting value for the efficiency of devices used to produce work from heat for our use. 

The second law of thermodynamics also consists of two parts. The first part is used to define a new thermodynamic variable called entropy, denoted by S. Entropy is the measure of a system s energy that is unavailable for work.The first part of the second law says that if a reversible process i f takes place in a system, then the entropy change of the system can be found by adding up the heat added to the system divided by the absolute temperature of the system when each small amount of heat is added ... 

Thus, in adiabatic processes the entropy of a system must always increase or remain constant. In words, the second law of thermodynamics states that the entropy of a system that undergoes an adiabatic process can never decrease. Notice that for the system plus the surroundings, that is, the universe, all processes are adiabatic since there are no surroundings, hence in the universe the entropy can never decrease. Thus, the first law deals with the conservation of energy in any type of process, while the sec-... 

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