Entropy change reversible

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. ... 

The entropy change of any. system and its. surroundings, considered together, re.sulting from any real proce.s.s is positive, approaching zero when the proce.s.s approaches reversibility. 

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... 

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 ... 

The entropy change of a system during any process depends only upon its initial and final states and not upon the path of the process by which it proceeds from its initial to its final state. Thus one can devise a reversible idealized process to restore a system to its initial state following a change and thereby determine AS =... 

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. 

In a Carnot s cycle, the entropy Qi/Ti is taken from the hot reservoir, and the entropy Q2/T2 is given up to the cold reservoir, and no other entropy change occurs anywhere else. Since these two quantities of entropy are equal and opposite, the entropy. change in the hot reservoir is exactly balanced, or, to use an expression of Clausius, is compensated by an equivalent change in the cold reservoir. Again, in any reversible cycle there is on the whole no production of entropy so that all the changes are compensated. 

Example.—If a mol. of an ideal gas changes reversibly from a state of 10 litres at 15° C. to 100 litres at 50° C, show that the increase of entropy is... 

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 entropy changes ASa and ASB can be calculated from equation (2.69), which applies to the isothermal reversible expansion of ideal gas, since AS is independent of the path and the same result is obtained for the expansion during the spontaneous mixing process as during the controlled reversible expansion. Equation (2.69) gives... 

To derive an expression for the change in entropy when a system is heated, we first note that Eq. 1 applies only when the temperature remains constant as heat is supplied to a system. Except in special cases, that can be true only for infinitesimal transfers of heat so we have to break down the calculation into an infinite number of infinitesimal steps, with each step taking place at a constant but slightly different temperature, and then add together the infinitesimal entropy changes for all the steps. To do this is we use calculus. For an infinitesimal reversible transfer dgrev at the temperature T, the increase in entropy is also infinitesimal and, instead of Eq. 1, we write... 

By considering the total entropy change, we can draw some far-reaching conclusions about processes going on in the universe. For instance, we saw in Section 6.3 that maximum work is achieved if expansion takes place reversibly, by matching the... 

Calculate the entropy change for reversible heat transfer (Example 7.1). 

A change in entropy is equal to the heat supplied reversibly to a system divided by the temperature at which the transfer takes place, entropy of vaporization (AS ) The entropy change per mole accompanying vaporization (the conversion of a substance from the liquid state into the vapor state). 

Continuing the process we may now change the pressure on the gas to the vapor pressure of the glass as given by (12) and then carry out a reversible condensation. These steps will be seen to involve the entropy change... 

Entropy can be described by considering a closed system undergoing a reversible process. The entropy change, dS, of the system is defined by the relationship... 

In most processes, a reversible absorption of heat is accompanied by a change in temperature, and a calculation of the corresponding entropy change requires an evaluation of the integral of q/T. The term q is related to the heat capacity of the system which is usually expressed as a function of temperature. In a constant volume process, for example, the entropy change is... 

At a constant pressure, the entropy of any pure substance can be calculated for any temperature through the use of the procedure that is herein being described. The entropy change taking place during an isothermal reversible process, it may be recalled, is equal to the heat change involved divided by the absolute temperature ... 

If the system is neither closed nor thermally insulated, then the change in the entropy with time consists of two quantities of the time change in the entropy as a result of processes occurring within the system S and of entropy changes in the surroundings, caused by transfer of the entropy from the system in the reversible process Sc... 

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