Entropy constant-pressure processes

Thus, for constant pressure processes, the entropy increase is written as... 

Any characteristic of a system is called a property. The essential feature of a property is that it has a unique value when a system is in a particular state. Properties are considered to be either intensive or extensive. Intensive properties are those that are independent of the size of a system, such as temperature T and pressure p. Extensive properties are those that are dependent on the size of a system, such as volume V, internal energy U, and entropy S. Extensive properties per unit mass are called specific properties such as specific volume v, specific internal energy u, and specific entropy. s. Properties can be either measurable such as temperature T, volume V, pressure p, specific heat at constant pressure process Cp, and specific heat at constant volume process c, or non-measurable such as internal energy U and entropy S. A relatively small number of independent properties suffice to fix all other properties and thus the state of the system. If the system is composed of a single phase, free from magnetic, electrical, chemical, and surface effects, the state is fixed when any two independent intensive properties are fixed. 

While absolute entropy values can now be determined absolute values of Internal Energy and Enthalpy cannot be conceived. For ease of calculation, related especially to metallurgical reactions (constant pressure processes), a suitable reference point of enthalpy is conventionally chosen and that is - for pure elements, the enthalpy is zero when in Standard State . Standard... 

This equation gives the entropy difference between two states at the same pressure but at different temperatures. Since entropy is a state function, it does not matter whether the actual process that brought the system from the initial state to the final was a constant-pressure process, some more complicated... 

Calculate the entropy change for the following constant pressure process. 

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. 

In a constant pressure and entropy process, p — pexts and dp and dS are equal to zero so that equation (5.54) becomes... 

This important formula, which can be derived more formally from the laws of thermodynamics, applies when any change takes place at constant pressure and temperature. Notice that, for a given enthalpy change of the system (that is, a given output of heat), the entropy of the surroundings increases more if their temperature is low than if it is high (Fig. 7.16). The explanation is the sneeze in the street analogy mentioned in Section 7.2. Because AH is independent of path, Eq. 10 is applicable whether the process occurs reversibly or irreversibly. 

The entropy change of the surroundings due to a process taking place at constant pressure and temperature is equal to —AH/T, where AH is the change in enthalpy of the system. 

Second, the process must occur at constant pressure. Then we can relate the enthalpy change for the system to the entropy change for the surroundings. Recall thatZlH equals q when P is constant ... 

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 ... 

Cp is the specific heat at constant pressure, k is the compressibility at constant temperature. The conversion process of a second-order phase transition can extend over a certain temperature range. If it is linked with a change of the structure (which usually is the case), this is a continuous structural change. There is no hysteresis and no metastable phases occur. A transformation that almost proceeds in a second-order manner (very small discontinuity of volume or entropy) is sometimes called weakly first order . 

If an isobaric temperature change is carried out reversibly, the heat exchanged in the process can be substituted into the expression for the entropy change, and the equations at constant pressure when no work is performed other than PV work are... 

Substitution of Eq. (2.6) into (2.8) gives as a useful relationship between the entropy and enthalpy for constant pressure and temperature processes ... 

Under the general conditions of constant pressure and temperature, the sum of the changes in the magnitude of the enthalpy and the entropy during any process determines the overall change in the Gibbs free energy of the system ... 

AG ° and AG are expressions of the maximum amount of free energy that a given reaction can theoretically deliver—an amount of energy that could be realized only if a perfectly efficient device were available to trap or harness it. Given that no such device is possible (some free energy is always lost to entropy during any process), the amount of work done by the reaction at constant temperature and pressure is always less than the theoretical amount. 

The total entropy change, AStot, is the sum of the changes in the system, AS, and its surroundings, ASsurr, with AStot = AS + ASsurr. For a process at constant pressure and temperature, the change in the entropy of the surroundings is given by Eq. 11, ASvllrr = —AH/T. Therefore, under these conditions,... 

The entropy of fusion in cal deg-1 g-1 is easily computed from the data of Table 3 by dividing the heats of fusion by the absolute temperature of the melting point. For theoretical reasons in many cases it is interesting to know the entropy of fusion at constant volume. Thus, the total measured entropy of fusion at constant pressure and composition, ASf, must be corrected for the gain in entropy due to the volume increase on fusion. The fusion process may be imagined as occurring at... 

When a system undergoes a process at a constant pressure, does the entropy change depend on the temperature ... 

The mixing of substances is an irreversible process that takes place creating entropy in the system. The entropy thus created is defined as the entropy of mixing SM. Suppose two different ideal gases with different volumes Vl and V2 are mixed isothermally at a constant pressure p to make a single mixture system with a volume V, + V2 as shown in Fig. 3. 10. The overall entropy S1 of both individual systems before the mixing is obtained from Eq. 3.47 as shown in Eq. 3.49 ... 

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