3510_chap5 - Chapter 5 (Still Chapter 3 in 8th Ed.) The...

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1 Chapter 5 (Still Chapter 3 in 8 th Ed.) The Second Law of Thermodynamics (II)
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2 CHAPTER 5 OUTLINE SECTION 5.1 - The fundamental equation SECTION 5.2 - Properties of the internal energy SECTION 5.3 - General considerations SECTION 5.4 - The variation of the Gibbs energy with temperature SECTION 5.5 - The variation of the Gibbs energy with pressure HOMEWORK ASSIGNMENTS EXERCISES 5.5 - 5.9 PROBLEMS 5.1, 5.6
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3 The Fundamental Equation We have shown that: dU = dq + dw plus dw rev = - pdV and dq rev = TdS We may write: dU = TdS pdV (for constant composition)
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4 In chapter 3 we discussed total integrals. Properties of the internal energy dy y z dx x z dz x y + = We can express U as a function of S and V , i.e. U = f ( S,V ) If z = f ( x,y ) then: dV V U dS S U dU S V + = dU = TdS pdV c.f. T S U V = p V U S - = We have discovered that
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5 Properties of the internal energy Recall the test for exactness: dy y z dx x z dz Gdy Fdx x y + = = + If the differential is exact then: y x x G y F = All state functions have exact differentials
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6 dV V U dS S U dU GdV FdS S V + = = + Properties of the internal energy Therefore: Where: T S U F V = = p V U G S - = = Because this is exact we may write: V S S G V F = V S S p V T - = We have obtained our first Maxwell relation !
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7 Relationships between state functions: Be prepared! U
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3510_chap5 - Chapter 5 (Still Chapter 3 in 8th Ed.) The...

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