# (Q and/or W) A closed system is one that does not exchange matter with its surroundings, although it may exchange energy. dn i = 0(i = 1, 2, …..)(1.1)

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(Q and/or W)

A closed system is one that does not exchange matter with its surroundings, although it may exchange energy. dn i = 0(i = 1, 2, …..)(1.1) No internal energy transported across boundary. All energy exchange between a closed system and its surroundings appears as heat and work. The total energy change of the surroundings equals the net energy transferred to or from it as heat and work.

First and second laws of Thermodynamics: (1.2) For reversible process: (1.3) withT dS = dQ rev : heat absorbed by the system - P dV = dW rev : work done by the system If the interaction occurs irreversibly: (1.4)

The internal energy change can be calculated by integrating eq. (1.2): (1.5) For process occurring at constant S and V: (1.6) At constant S and V, U tends toward a minimum in an actual or irreversible process in a closed system, and remains constant in a reversible process. Eq. (1.6) provides a criterion for equilibrium in a closed system.

Definition: (1.7) Differentiating eq. (1.7) yields: Combining the above equation with eq. (1.3) leads to For a closed system at constant S and P : (1.8) (1.9)

the Helmholtz free energy (A) is a thermodynamic potential that measures the “useful” work obtainable from a closed system at a constant temperature and volume. –  A = the maximum amount of work extractable from a thermodynamic process in which temperature and volume are held constant. Under these conditions, it is minimized at equilibrium.

Definition: (1.10) Differentiating eq. (1.10) yields: Combining the above equation with eq. (1.3) leads to For a closed system at constant T and V : (1.11) (1.12)

Gibbs free energy (G) is a thermodynamic potential that measures the "useful" or process-initiating work obtainable from a thermodynamic system at a constant temperature and pressure (isothermal, isobaric). The Gibbs free energy is the maximum amount of non- expansion work that can be extracted from a closed system; this maximum can be attained only in a completely reversible process.

Definition: (1.13) Differentiating eq. (1.13) yields: Combining the above equation with eq. (1.8) leads to For a closed system at constant P and T : (1.14) (1.15)

If F = F(x, y), the total differential of F is: with (1.16)

Further differentiation yields Hence from equation: we obtain: (1.17)

Resume: (1.3) (1.8) (1.11) (1.14)

According to eq. (1.17): (1.18) (1.19) (1.20) (1.21)

(1.22) (1.23) Enthalpy As a function of P and T, we may express: Total differential of the above equation is (  H/  T) P is obtained from the definition of C P :

(1.25) (1.24) (  H/  P) T is derived from fundamental equation: (1.8) Differentiation with respect of P at constant T yields: Combining eq. (1.24) with Maxwell equation (1.21): Introducing eqs. (1.23) and (1.25) into eq. (1.22) results in : (1.26)

Kalau T konstan,

(1.27) Entropy As a function of P and T, we may express: Total differential of the above equation is (  S/  P) T is obtained from the Maxwell equation (1.21) (1.21)

(1.29) (1.28) (  S/  T) P is derived from fundamental equation: (1.8) Differentiation with respect of T at constant P yields: Combining eq. (1.23) with (1.28): Introducing eqs. (1.21) and (1.29) into eq. (1.27) results in : (1.30)

(1.31) Enthalpy of ideal gas From eq. (1.26) (1.32)

Entropy of ideal gas (1.33) From eq. (1.30)

Kalau sistem mengalami proses dari keadaan (T 1, P 1 ) ke (T 2, P 2 ), maka perubahan entropynya adalah: Jika C P konstan maka

The fundamental property relations for homogeneous fluids of constant composition given by Eqs. (1.3), (1.8), (1.11), and (1.14) show that each of the thermodynamic properties U, H, A, and G is functionally related to a special pair of variables. In particular (1.14) expresses the functional relation: Thus the special, or canonical variables for the Gibbs energy are temperature and pressure. Since these variables can be directly measured and controlled, the Gibbs energy is a thermodynamic property of great potential utility.

An alternative form of Eq. (1.14), a fundamental property relation, follows from the mathematical identity: Substitution for dG by Eq. (1.14) and for G by Eq. (1.13) gives: (1.34)

From eq. (1.34) (1.35) (1.36) When G/RT is known as a function of T and P, V/RT and H/RT follow by simple differentiation. The remaining properties are given by defining equations. In particular, and

Untuk T konstan, dT = 0 (T konstan)

Thus, when we know how G/RT (or G) is related to its canonical variables, T and P, i.e., when we are given G/RT = g(T, P), we can evaluate all other thermodynamic properties by simple mathematical operations. The Gibbs energy when given as a function of T and P therefore serves as a generating function for the other thermodynamic properties, and implicitly represents complete property information.

Unfortunately, no experimental method for the direct measurement of numerical values of G or G/RT is known, and the equations which follow directly from the Gibbs energy are of little practical use. However, the concept of the Gibbs energy as a generating function for other thermodynamic properties carries over to a closely related property for which numerical values are readily obtained. Thus, by definition the residual Gibbs energy is: where G and G ig are the actual and the ideal-gas values of the Gibbs energy at the same temperature and pressure. (1.37)

Other residual properties are defined in an analogous way. The residual volume, for example, is: The definition for the generic residual property is: Where M is the molar value of any extensive thermodynamic property, e.g., V, U, H, S, or G. Note that M and M ig, the actual and ideal-gas properties, are at the same temperature and pressure. (1.38) (1.39)

Equation (1.34), written for the special case of an ideal gas, becomes: Subtracting this equation from Eq. (1.34) itself gives: This fundamental property relation for residual properties applies to fluids of constant composition. Useful restricted forms are: (1.40) (1.41) (1.42)

( – )

In addition, the defining equation for the Gibbs energy, G = H – TS, may also be written for the special case of an ideal gas, G ig = H ig – TS ig ; by difference, The residual entropy is therefore: (1.43)

Thus the residual Gibbs energy serves as a generating function for the other residual properties, and here a direct link with experiment does exist. It is provided by Eq. (1.41), written: (constant T) Integration from zero pressure to arbitrary pressure P yields: (constant T) where at the lower limit G R /RT is equal to zero because the zero- pressure state is an ideal-gas state.

(T konstan) (1.41)

In view of Eq. (1.38): (constant T)(1.44) Differentiation of Eq. (1.44) with respect to temperature in accord with Eq. (1.42) gives (constant T)(1.45) The residual entropy is found by combination of Eqs. (1.43) through (1.45): (constant T)(1.46)

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