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(Q and/or W)

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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.

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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)

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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.

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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)

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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.

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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)

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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.

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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)

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

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

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

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

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(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 :

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(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)

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Kalau T konstan,

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(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)

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(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)

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

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

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

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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.

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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)

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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

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Untuk T konstan, dT = 0 (T konstan)

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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.

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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)

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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)

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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)

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( – )

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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)

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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.

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(T konstan) (1.41)

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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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