Second-law heats

Typically, the biggest lost that occurs in chemical processes is in the combustion step (6). One-third of the work potential of natural gas is lost when it is burned with unpreheated air. Eigure 3 shows a conventional and a second law heat balance. The conventional analysis only points to recovery of heat from the stack as an energy improvement. Second law analysis shows that other losses are much greater. 

Up until the late 1980 s measured activation energies for the reverse reaction were combined with assumed values of the forward reaction to give Second Law heats of formation for R [74]. However, the values of AfH (R) were found to be incompatible with those measured by addition (or recombination)/dissociation equilibria [71, 75]. The reasons for this were rationalized by a series of experiments performed by Gutman and coworkers [76, 77] and others [78, 79] who directly measured the rate... 

Cl(g) ZnCl(g). The reported a second law heat (ZrCl)/I(Cl) which we calculated from... 

The first law of thermodynamics (the energy of the universe is constant) implies that the energy function U is independent of path. As a consequence of the second law (heat does not of itself flow from a body of lower temperature to one of higher temperature), the entropy function S can be shown to be independent of path. For a pure component or a mixture at constant composition, both the first and second laws are contained in the expression... 

Using the relation between the chemical potential and enthalpy /x, = / , — Tsj = m, + Pv, — Ps, we can relate the second law heat flow J", the conduction energy flow J , and the pure heat flow as follows ... 

There are many equivalent statements of the second law, some of which involve statements about heat engines and perpetual motion machines of the second kind that appear superficially quite different from equation (A2.T21). They will not be dealt with here, but two variant fonns of equation (A2.T21) may be noted in... 

If FCCU operations are not changed to accommodate changes ia feed or catalyst quaUty, then the amount of heat required to satisfy the heat balance essentially does not change. Thus the amount of coke burned ia the regenerator expressed as a percent of feed does not change. The consistency of the coke yield, arising from its dependence on the FCCU heat balance, has been classified as the second law of catalytic cracking (7). 

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. 

In the broadest sense, thermodynamics is concerned with mathematical relationships that describe equiUbrium conditions as well as transformations of energy from one form to another. Many chemical properties and parameters of engineering significance have origins in the mathematical expressions of the first and second laws and accompanying definitions. Particularly important are those fundamental equations which connect thermodynamic state functions to real-world, measurable properties such as pressure, volume, temperature, and heat capacity (1 3) (see also Thermodynamic properties). 

Since heat transfer with respec t to the surroundings and with respect to the system are equal but of opposite sign, = —Q. Moreover, the second law requires for a reversible process that the entropy changes of system and surroundings be equalbut of opposite sign AS = —AS Equation (4-356) can therefore be written Q = TcAS In terms of rates this becomes... 

Hence, the second-law efficiency of the expander-heat-exchanger-compressor system is p p... 

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... 

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... 

Meunier, F., Second law analysis of a solid adsorption heat pump operating on reversible cascade cycles application to the zeolite-water pair. Heat Recovery Systems, 1985, 5, 133 141. 

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 maximum temperature difference that takes place in a heat exchanger is T /, - 7. A higher temperature difference cannot occur due to the second law theoretical heat transfer rate in a heat exchanger is... 

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... 

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. 

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