ENG_sgwhk08 - Definition of entropy () For any closed...

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1 Definition of entropy ( 熵的定义 ) For any closed system, it exists at equilibrium a single valued state function called entropy , denoted S , which is an extensive quantity . When the system is changed from equilibrium A to equilibrium B, the entropy increment Δ S equals the algebraic sum of the quotient of heat over temperature in any reversible processes , i.e., ( δ Q R ) i is the infinitesimal quantity of energy supplied as heat to the system reversibly at a temperature T i . () ( ) i i Q SS B S A T δ Δ= =
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2 Entropy augmenting principium ( 熵增加原理 ) For a closed system from equilibrium A to equilibrium B, the entropy of system does not automatically decrease forever. The entropy does not change in an adiabatic reversible process, and augments in an adiabatic irreversible process, i.e., Δ S = S (B)- S (A) 0 { } > adiabatic irreversible = adiabatic reversible Deduction The entropy of an insulated system does not automatically decrease forever; the entropy does not change in reversible processes, and augments in irreversible processes ( Δ S ) insulated = Δ S (B)- Δ S (A) 0 { } > irreversible = reversible
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3 dS=d e S + d i S d e S ⎯⎯ Entropy flow( 熵流 ). It is the entropy flow entering into the system when the system exchanges energy and substance with the surroundings through the boundary Σ , it has not defined positive or negative symbol d i S ⎯⎯ Entropy production( 熵产生 ). It is the entropy production due to irreversible processes inside the system (such as diffusion, heat exchange, chemical reactions, etc.) Any system at equilibrium has a state function, the entropy, which is extensive quantity. The entropy increment of system undergone any process consists two contributions , i.e.,
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4 Entropy production principium ( 熵产生原理 ) The entropy production inside a system could not never be negative. It is zero in reversible processes, and is always above zero in irreversible processes , i.e., d i S 0 { } > irreversible = reversible The equilibrium equation of entropy for any system dS / dt = Σ ( 1 / T ) δ Q i / dt + Σ S j dn j / dt + d i S / dt
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5 If T sur is constant sys sur heat source engin sur Q SS S T Δ= Δ + Δ = sys Heat source Heat source sur sur (- δ ) δ d = or Δ =- QQ TT Here δ Q Heat source =- δ Q sys We assume that each heat source is very huge, and with constant volume and at fixed uniform temperature it is that the change of the heat source is always reversible, thus Calculation of the change in entropy of the surroundings ( 环境熵变的计算 )
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6 Starting from T Q S r δ d = For isothermal processes T Q T Q S r r δ = = Δ Calculation of entropy change in isothermal processes ( 等温过程熵变的计算 ) If S = S ( , ) dV V S dT T S dS T V + = For closed systems of fixed composition without other works
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7 Isothermal process d T =0 If S = S ( , p ) dp p S dT T S dS T p + = For isothermal process d T =0 TV Sp dS dV dV VT ∂∂ ⎛⎞ == ⎜⎟
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This note was uploaded on 05/25/2011 for the course CHEMISTRY 001 taught by Professor Tian during the Spring '11 term at Xiamen University.

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ENG_sgwhk08 - Definition of entropy () For any closed...

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