Reversible process, entropy change

Obviously die first law is not all there is to the structure of themiodynamics, since some adiabatic changes occur spontaneously while the reverse process never occurs. An aspect of the second law is that a state fimction, the entropy S, is found that increases in a spontaneous adiabatic process and remains unchanged in a reversible adiabatic process it caimot decrease in any adiabatic process. 

There exists a propei ty called entropy, which for systems at internal equilihnum Is an intnnsic propeity of the system, functionally related to the measurable coordinates which characterize the system. For reversible processes, changes in this propeity may be calculated by the equation ... 

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... 

State is adiabatic and reversible. Such an adiabatic reversible process is called an isentropic state change one in which the entropy remains constant. 

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 ... 

This leads to what is called the Clausius form of the second law of thermodynamics. No processes are possible whose only result is the removal of energy from one reservoir and its absorption by another reservoir at a higher temperature. On the other hand, if energy flows from the hot reservoir to the cold reservoir with no other changes in the universe, then the same arguments can be used to show that the entropy increases, nr remains constant for reversible processes. Therefore, such energy flows, which arc vciy familiar, are in agreement with the laws of thermodynamics. 

For any reversible process, the sum of the changes in entropy for the system and its surroundings is zero. All natural or real processes are irreversible and are accompanied by a net increase in entropy. 

Alternatively, for an ideal reversible process, the sum of all the changes in entropy-must be zero or... 

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. 

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 calculate a change in entropy for a process we find a reversible path between the initial and final states. It is immaterial whether the actual process is irreversible or reversible. Because entropy is a state function, the change for that path will be the same as that for the irreversible path. 

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... 

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... 

The simplest process involving a change in entropy is a reversible process occurring at a constant temperature, T. For such a process, the change in entropy, AS, can be expressed as... 

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... 

The law implies that for a reversible process, the sum of all changes in entropy, taken over all the systems participating in the process, AAtot, is zero. 

The sum is equal to zero for reversible processes, where the system is always under equilibrium conditions, and larger than zero for irreversible processes. The entropy change of the surroundings is defined as... 

Entropy is the ratio of a body s energy to its temperature according to the Clausius equality (as defined in the next section). For a reversible process, the change in entropy is defined by... 

For a reversible process A5universe = 0. The qualitative entropy change (increase or decrease of entropy) for a system can sometimes be determined using a few simple rules ... 

The van t Hoff plots for thermal denaturation of proteins are linear in the transition region, thus allowing the enthalpy change (AHm) of unfolding at the transition temperature (Tm) to be estimated. Because of the change in free energy in (AG) = 0 at Tm (reversible process), the entropy of unfolding (ASm) at the transition midpoint can be calculated from ... 

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