As shown in the figure, the molar entropy of a pure substance increases with increasing temperature. In chemical handbooks we see the tabulated numerical values of the molar entropy calculated for a number of pure substances in the standard state at temperature K and pressure Note that the molar entropy thus calculated based on the third law of thermodynamics is occasionally called "absolute" entropy.
Molar entropy of a pure substance as a function of temperature. Entropy of Heat Transfer.
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Let us now consider a steady flow of heat dQ irr that occurs irreversibly between a phase at a high temperature T1 and a phase at a low temperature T 2 in a closed system as shown in Fig. In this case the irreversibly created entropy is continuously released from the low temperature phase to the surroundings so that no accumulation of created entropy occurs in the system.
Thermodynamics of Mixing and Dilution - Chemistry LibreTexts
Irreversible steady flow of heat from phase 1 at high temperature 7"1to phase 2 at low temperature T2 in a closed system. Heat transfer between two different temperatures can be carried out in a reversible way by using a reversible heat engine or heat pump. In this case, however, a part of the transferring heat converts into work or a part of the transferring heat is created by work. The heat engine is a closed system of a gas, in which a quantity of heat dQl is absorbed from an outside heat source at a high temperature T1 and preforms a quantity of work dW to the exterior of the system releasing a quantity of heat dQ2 less than dQ1 into an outside heat reservoir at a low temperature T2.
On the other hand, a closed system of a gas is called a heat pump or an inverse heat engine, when it receives a quantity of work dW from the outside and takes up a quantity of heat dQ2 from an outside heat reservoir at a low temperature T2 bringing a quantity of heat dQ1 more than dQ2 into an outside heat reservoir at a high temperature T1.
One of the ideal heat engines operating in a reversible way is known as Carnot's heat engine, in which two adiabatic and two isothermal processes constitute what is called the Carnot cycle. High Low High Low temperature temperature temperature temperature i iii! Processes occurring in a heat engine and in a heat pump This type of reversible heat transfer by means of a heat engine has its affinity A, which is equivalent to the maximum work W obtainable with the engine as expressed by Eq.
Thermodynamics Free Energy Chemical Substances
Isothermal expansion of one mole of an ideal gas resulting in an entropy increase. Entropy of Gas Expansion. Let us now discuss the entropy of gas expansion in a closed system. If the gas expansion takes place isothermally as shown in Fig. 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 S M. Entropy of mixing of two gases to form a gas mixture at constant pressure and temperature. The second law of thermodynamics indicates that all irreversible processes advance in the direction of creating entropy and decreasing affinity. This chapter examines the property affinity in chemical reactions and the relation between the affinity and various other thermodynamic quantities. Affinity in Chemical Reactions.
The concept of affinity introduced in the foregoing chapter section 3. Let us now discuss the physical meaning of the affinity of chemical reactions. As mentioned in the foregoing, we have in Eq. The inequality equation 4. In Eqs.
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Irreversible reaction ffi ty Fig. Affinity in a chemical reaction. If the affinity is zero A - 0, no irreversible reaction advances and the system is in equilibrium. Then the equations from 4. Affinity and Heat of Reaction. Equations 3. For multiple reactions occurring simultaneously in the system the third term on the right hand side of Eq. Since the interaction between reaction i and reaction j is given in Eq. The A v e r a g e Heat of Reaction. Integrating Eq. For a system at constant temperature and volume, as described in Eqs.
The reaction is exothermic heat-releasing when the heat of reaction is negative, while it is endothermic heat-absorbing when the heat of reaction is positive. Similarly, for a chemical reaction at constant temperature T and pressure p Eqs. The physical quantity that we usually call the affinity of a reaction corresponds to the average affinity of the reaction.
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Furthermore, from Eq. Equation 4. If we integrate Eq. We have usually to assume that the partial molar capacities of substances in the reaction system are equal to the molar heat capacities in the pure state. At temperature T o, we have from Eq. For open systems permeable to heat, work, and chemical substances, the chemical potential can be used more conveniently to describe the state of the systems than the usual extensive energy functions.
This chapter discusses the characteristics of the chemical potential of substances in relation with various thermodynamic energy functions. In a mixture of substances the chemical potential of an individual constituent can be expressed in its unitary part and mixing part. Thermodynamic Potentials in Open Systems.
We have introduced in the foregoing chapters energy functions thermodynamic potentials of extensive properties such as U, H, F, and G to describe the thermodynamic state of a closed system which forbids the exchange of substances with its surroundings. For an open system which allows the exchange of substances to occur with the surroundings, it is often convenient to use energy functions of intensive properties such as the partial molar quantities of energy rather than thermodynamic energy functions of extensive properties.
For a closed system the first law of thermodynamics has defined an energy function called internal energy U, which is expressed as a function of the temperature, volume, and number of moles of the constituent substances in the system; U - U T, V, n Thermodynamics presumes that the functions U T,V, nl The energy functions of U, H, F, and G, then, apply not only to closed systems but also to open systems.
The total differentials of the other energy functions H, F, and G can also be expressed in the form similar to Eq. We shall now choose S, V, n l. The internal energy of an open system then yields its total differential d U expressed as a function of these independent variables as shown in Eq. The chemical potential of a substance in a system. Chemical Potentials and the Affinity of Reaction. We thus obtain Eq. As the reaction reaches its equilibrium, the affinity of the reaction decreases to zero as shown in Eq. The most important property of the chemical potential is that the affinity of a reaction is expressed by the difference in the chemical potential between the reactants and the products as shown in Eq.
At a constant temperature and pressure we then obtain Eq. Chemical Potentials of Substances in Ideal Mixtures.
As mentioned in the foregoing chapters, the mixing of substances causes an increase in entropy of the system and hence changes the chemical potentials of the substances Generally, the chemical potential of a constituent substance i in a mixture consists of a u n i t a r y p a r t , which is inherent to the pure substance i and independent of its concentration, and a c o m m u n a l p a r t , which depends on the concentration of constituent i [Ref.
The communal part of the chemical potential of a constituent i in a mixture arises from the entropy of mixing of i: For an ideal mixture the molar entropy of mixing of i, sff, is given from Eq. We then express the chemical potential of substance i in a mixture as shown in Eq. The communal part, RTln x i , on the right hand side of Eq.
A mixture can thus be called ideal, if the chemical potential of the constituent substances, i, in the system varies linearly with the logarithm of the molar fraction of i at the ratio of RT. The linear relation of Eq. If we use the concentration scale of molality m instead of mole fraction x, the chemical potential of a solute constituent i is expressed by Eq. Activity and Activity Coefficient. For a non-ideal mixture in which Eq. We then have Eq. Chemical Potentials of Pure Substances.
The chemical potential of a pure substance i indicates the thermodynamic energy level of the substance relative to the energy level of the chemical elements that make up the substance i. In chemical thermodynamics the chemical potentials of elements are conventionally all set zero in the stable state of them at the standard temperature K and pressure The chemical potential of a substance a chemical c o m p o u n d i at the standard state, as a result, is equal to the free enthalpy Gibbs energy required to form one mole of the substance i from its constituent elements in their stable standard state.
Table 5. Thermodynamic P o t e n t i a l s in Ideal M i x t u r e s Starting from the definition 5.
Related Thermodynamics and the free energy of chemical substances
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