Exam 2 equation sheet spring 2011

Exam 2 equation sheet spring 2011 - = = K k k N dt dN 1 ....

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Thermodynamics I Exam 2 Equation Sheet Entropy equation: Rate of change: = + + = K k gen k k S T Q S M dt dS 1 . . . Integrated: gen t t k t t k k S dt T Q dt S M S S + + = - 2 1 2 1 . . 1 2 Special Cases (ideal gas, constant heat capacities): + = - 1 2 1 2 1 2 ln ln V V R T T C S S IG V - = - 1 2 1 2 1 2 ln ln P P R T T C S S IG P + = - 1 2 1 2 1 2 ln ln P P C V V C S S IG V IG P Special Cases (incompressible solid or liquid): = - 2 1 1 2 T T P T dT C S S Efficiency: Heat engine: H Q W - = η Carnot heat engine: - = - = H C H H T T T Q W Definitions: p p T H C v v T U C PV U H + = For Ideal Gases: nRT PV = = dT C H p = dT C U v R T C T C IG V IG P + = ) ( ) ( Special Case: (solid, liquid, or gas) 1) Constant volume, constant C v : T C U v = 2) Constant pressure, constant C p : T C H p = Pressure Gauge: g A M M P p w g + = Spring (Hooke’s law):
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x k F - = 2 2 1 kx E P = Work: Electrical shaft work: EI W S = Expansion / compression work: dt dV P W - = . Mass balances: = = K k k M dt dM 1 . = = - K k k M t M t M 1 . 1 2 ) ( ) ( Mole balance:
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Unformatted text preview: = = K k k N dt dN 1 . Energy Balance: Rate of change: . . 1 2 . 2 2 2 W Q gh H M gh M U dt d k K k k + + + + = + + = . . 1 2 . 2 2 2 W Q gh m H N gh Nm U dt d k K k k + + + + = + + = Integrated: W Q dt gh H M gh M U gh M U k K k t t k t t + + + + = + +- + + = 1 2 . . 2 2 2 2 2 2 1 1 2...
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Exam 2 equation sheet spring 2011 - = = K k k N dt dN 1 ....

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