Notes_19_theTds_Equations

Notes_19_theTds_Equations - Meeting 18, Sections 7-77-9 The...

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1 Meeting 18, Sections 7-7–7-9 The Tds Equations
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What we covered Wednesday The Clausius Inequality A new property: entropy Entropy balance Entropy generation Obtaining entropy values Isentropic processes The Ts diagram 2
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Topics for today Obtaining entropy values for other “substances.” TER Incompressible substances Ideal Gases Constant Specific Heats Variable Specific Heats Isentropic processes Constant Specific Heats Variable Specific Heats 3
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4 The only distinguishing property of a TER is T. They can give up or absorb an infinite about of energy. They undergo internally reversible processes. Entropy change of a thermal reservoir
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5 Entropy change of a thermal reservoir For a thermal reservoir, heat transfer occurs at constant temperature…the reservoir doesn’t change temperature as heat is removed or added: = T Q S δ Since T=constant: T Q S =
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6 Derivation of Tds equations: δ Q – δ W = dU For a simple closed system with boundary work: δ W = PdV The (reversible) work is given by: δ Q = dU + PdV Substituting gives: Taking the differential form of Q-W=ΔU
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7 More derivation…. For a reversible process: TdS = δ Q Make the substitution for Q in the energy equation: PdV + dU = TdS Or on a per unit mass basis: Pdv + du = Tds
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8 Entropy is a property. The Tds expression that we just derived expresses entropy in terms of other properties. The properties are independent of path….We can use the Tds equation we just derived to calculate the entropy change between any two states: Tds = du +Pdv Tds = dh - vdP Starting with enthalpy, it is possible to develop a second Tds equation: Tds Equations
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9 Let’s look at the entropy change for an incompressible substance: dT T ) T ( c ds = We start with the first Tds equation: Tds = cv(T)dT + Pdv For incompressible substances, v  const, so dv = 0. We also know that cv(T) = c(T), so we can write:
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10 Entropy change of an incompressible substance dT T ) T ( c s s 2 1 T T 1 2 = - 1 2 1 2 T T ln c s s = - Integrating If the specific heat does not vary with temperature: Why does this matter? This equation gives an algebraic expression to evaluate entropy change. Use this when tables are not available or when doing programming.
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A 20-kg aluminum block initially at 200 ºC is brought into contact with a 20-kg block of iron at 100 ºC in an insulated enclosure. Determine the final equilibrium temperature and the total entropy change for this process. 11
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This note was uploaded on 10/04/2011 for the course MEEN 315 taught by Professor Ramussen during the Summer '07 term at Texas A&M.

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Notes_19_theTds_Equations - Meeting 18, Sections 7-77-9 The...

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