Entropy change heating

Equation (3.7) gives a simple procedure for evaluating the entropy change accompanying a change of state. At the normal boiling point of a liquid, for example, the heat is absorbed reversibly and equals the heat of vaporization AH,. Since T is constant, the entropy of vaporization is AH,/T. For benzene, for example, AS, = (30.8 k J mol" )/353 = 87 J K mol. ... 

A heat engine is a device operating in cycles that takes in heat, from a heat reservoir at temperature Tp, discards heat, to another heat reservoir at a lower temperature T, and produces work. A heat reservoir is a body that can absorb or reject unlimited amounts of heat without change in temperature. Entropy changes of a heat reservoir depend only on the absolute temperature and on the quantity of heat transferred, and are always given by the integrated form of equation 4 ... 

Here, is replaced by because the effect of heat transfer on a heat reservoir does not depend on its reversibiUty. Thus the entropy changes of the two heat reservoirs associated with a heat engine are given by equations 6 and 7 ... 

Because the engine operates in cycles, it experiences no change in its own properties therefore the total entropy change of the engine and its associated heat reservoirs is given by equation 8 ... 

The entropy change AS/ - and the volume change AV/ - are the changes which occur when a unit amount of a pure chemical species is transferred from phase I to phase v at constant temperature and pressure. Integration of Eq. (4-18) for this change yields the latent heat of phase transition ... 

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... 

In these examples tire entropy change does not vaty widely, and the value of the equilibrium constant is mainly determined by the heat of dissociation. It can be concluded, tlrerefore, that niuogen is one of the most stable diatomic molecules, and tlrat chlorine is tire most stable diatomic halogen molecule. 

The small value of the entropy change reflects the fact that only liquids are involved in tlris reaction. The heat balance in canying out tlris reaction may be calculted, according to Hess s law, by calculating tire heat change at room temperarnre, and subtracting tire heat required to raise the products to the hnal teirrperamre. The data for tlris reaction are as follows ... 

Further information on the effect of polymer structure on melting points has been obtained by considering the heats and entropies of fusion. The relationship between free energy change AF with change in heat content A// and entropy change A5 at constant temperature is given by the equation... 

If the heat capacity can be evaluated at all temperatures between 0 K and the temperature of interest, an absolute entropy can be calculated. For biological processes, entropy changes are more useful than absolute entropies. The entropy change for a process can be calculated if the enthalpy change and free energy change are known. 

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 ... 

It must be emphasised that the heat q which appears in the definition of entropy (equation 20.137) is always that absorbed (or evolved) when the process is conducted reversibly. If the process is conducted irreversibly and the heat absorbed is q, then q will be less than q, and q/T will be less than AS the entropy change (equation 20.137). It follows that if an irreversible process takes place between the temperatures Tj and 7 , and has the same heat intake q at the higher temperature 7 2 as the corresponding reversible process, the efficiency of the former must be less than that of the latter, i.e. 

The Number of Dipoles per Unit Volume. The Entropy Change Accompanying Proton Transfers. The Equilibrium between a Solid and Its Saturated Solution. Examples of Values of L and AF°. The Change of Solubility with Temperature. Uni-divalent and Other Solutes. Lithium Carbonate in Aqueous Solution. H2COj in Aqueous Solution. Comparison between HjCOj and Li2C03 in Aqueous Solution. Heats of Solution and the Conventional Free Energies and Entropies of Solution. 

Table III presents integral excess entropies of formation for some solid and liquid solutions obtained by means of equilibrium techniques. Except for the alloys marked by a letter b, the excess entropy can be taken as a measure of the effect of the change of the vibrational spectrum in the formation of the solution. The entropy change associated with the electrons, although a real effect as shown by Rayne s54 measurements of the electronic specific heat of a-brasses, is too small to be of importance in these numbers. Attention is directed to the very appreciable magnitude of the vibrational entropy contribution in many of these alloys, and to the fact that whether the alloy is solid or liquid is not of primary importance. It is difficult to relate even the sign of the excess entropy to the properties of the individual constituents.

Equation (2.38) relates an entropy change to the flow of an infinitesimal quantity of heat in a reversible process. Earlier in this chapter, we have shown that in the reversible process, the flow of work 6 ir is a minimum for the reversible process.51 Since ir and q are related through the first law expression... 

The Caratheodory analysis has shown that a fundamental aspect of the Second Law is that the allowed entropy changes in irreversible adiabatic processes can occur in only one direction. Whether the allowed direction is increasing or decreasing turns out to be inherent in the conventions we adopt for heat and temperature as we will now show. 

Adiabatic processes are examples of (d). If a mole of ideal gas is allowed to expand adiabatically into an evacuated bulb to twice its initial volume, the entropy of the gas increases by 5.76 J K-1 mol-1. No entropy change occurs in the surroundings, since there is no exchange of heat. Hence, 5.76 J K-1 mol-1 is the net increase in entropy in the universe. 

E3.7 A block of copper weighing 50 g is placed in 100 g of HiO for a short time. The copper is then removed from the liquid, with no adhering drops of water, and separated from it adiabatically. Temperature equilibrium is then established in both the copper and water. The entire process is carried out adiabatically at constant pressure. The initial temperature of the copper was 373 K and that of the water was 298 K. The final temperature of the copper block was 323 K. Consider the water and the block of copper as an isolated system and assume that the only transfer of heat was between the copper and the water. The specific heat of copper at constant pressure is 0.389 JK. g l and that of water is 4.18 J-K 1-g 1. Calculate the entropy change in the isolated system. 

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