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ENG_sgwhk09

ENG_sgwhk09 - IX Fundamental equation of closed system The...

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1 IX. Fundamental equation of closed system ( 封闭体系的 基本公式 ) The 1 st law gives dU = δ Q + δ W exp + δ W’ when there is no other work δ W’=0 dU = δ Q + δ W exp in a reversible process δ Q = δ Q R = TdS and δ W exp =-pdV We obtain the fundamental equation: dU = TdS - pdV For any processes dU= δ Q + δ W exp = TdS - pdV In reversible processes δ Q = TdS δ W exp = -pdV In irreversible processes δ Q < TdS δ W exp > - pdV Any processes without other work

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2 X. The change in Entropy of chemical reactions ( 化学反应的熵变 ) The change in entropy of chemical reaction can be also obtained by designing a reversible route, and to calculate the sum of quotient of heat over temperature in this route. However, since the establishment of the third law of thermodynamics, the data of “absolute” entropy (calorimetric entropy) of each substance can be found in list of thermodynamic data. It lists often the data at 1 standard pressure p Θ and at 298.15K. Using the temperature dependence of heat capacity we can calculate the change in entropy of chemical reaction at other temperature. -9 th lecture-
3 The standard reaction entropy, : the difference between the molar entropies of the pure, separated products and the pure, separated reactants, all substances being in their standard states at the specified temperature. S r Δ m Reactants m Products r S ν S ν S = Δ rB m (B) S ν S Δ= v -stoichiometric coefficient For a reaction B 0 ν B =

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4 Example 8 Evaluate the change in standard molar entropy of the chemical reaction below ) , 298 , ( ) , 298 , ( ) , 298 , ( 2 4 2 5 2 Θ Θ Θ + p K g O H p K g H C p K g OH H C 1 1 6 2 . . 59 . 282 ) 298 , , ( Θ = mol K J K g OH H C S m Known 1 1 4 2 . . 45 . 219 ) 298 , , ( Θ = mol K J K g H C S m 1 1 2 . . 74 . 188 ) 298 , , ( Θ = mol K J K g O H S m Solution = Δ Θ m S + Θ ) 298 ( 4 2 K , g , H C S m ) 298 ( 2 K , g , O H S m Θ 1 1 6 2 J 60 125 298 Θ = mol . K . . K , g , OH H C S ) ( m
5 XI. Calculation of the entropy change of simple PVT systems ( 简单 PVT 体系过程熵变的计算 ) For a given quantity of single phase pure substance, or a given quantity of multi-component system of fixed composition, it needs only two independent state variables to determine the state of the system, so we can use two formulas below to do calculations: ( ) p , T S S = ( ) V , T S =

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6 (1) From S=S ( T,p ) From the basic formula of closed system dU=TdS-pdV From H=U+pV dH=dU+d(pV)=TdS-pdV+Vdp+pdV+dpdV=TdS+Vdp So, dp T V T dH dS = A given quantity of single phase pure substance, or of multi- component system of fixed composition (no phase change, no chemical reaction) no other work. since H=H(T,p) dp p H dT T H dH T p + = Introduce it into the above equation dp p S dT T S dS T p + = (1)
7 dp T V dp p H T dT T H T dS T p + = 1 1 dp V p H T dT T C dS T p + = 1

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ENG_sgwhk09 - IX Fundamental equation of closed system The...

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