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Chapter 4. Heat effect-student

Chapter 4. Heat effect-student - Chapter 4 Heat Effects In...

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In two circumstances 0 ) ( = dV V U T Will be true 1. Constant volume 2. U is independent on V. This is exactly true for ideal gases and incompressible fluids and approximately true for low pressure gases The equation should meet the following requirements: mechanically reversible, constant-volume process, closed-system, both E P and E K are negligible and Ws =0 = = 2 1 T T V dT C U Q For Chapter 4. Heat Effects
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In two circumstances 0 ) ( = dP P H T will be true 1. Constant pressure process 2. H is independent on P. This is exactly true for ideal gases approximately true for low pressure gases = = 2 1 T T P dT C H Q For The equation should meet the following requirements: mechanically reversible, constant-volume process, closed-system, both E P and E K are negligible and W s =0
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We need relation of C with T, i.e. C = f (T). A popular empirical equation: C P /R is dimensionless so C P has the same unit as R The real gas becomes ideal in limit as P 0. If it remains ideal when compressed to a finite pressure, it would be hypothetical ideal gas. For this type of gases, C p ig and C V ig are therefore different for different gases (being affected by their chemical natures) Table C.1 gives the constants A, B, C, and D for different gases in the ideal-gas state
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For ideal gases, w e have known from Eq (3.19) This means that C V and C P follow the same trend with T The molar heat capacity of the mixture in the ideal-gas state: For liquid and solid, dependences of C P and C V on temperature are found by experiments. Table C.2 and C.3 give some C P , C V , A, B, C and D data.
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( 29 0 2 0 2 2 0 0 2 2 ) 1 ( 3 ) 1 ( 2 ) ( 0 0 T T T D T C T B A dT DT CT BT A dT R C T T T T P - + + + + + + = + + + = - τ τ τ τ 0 T T τ These equations can be used to evaluate H P C With 2 0 2 2 0 0 ) 1 ( 3 ) 1 ( 2 T D T C T B A R C H P τ τ τ τ + + + + + + = A starting estimated T allows evaluation of H P C of this value to (4.10), obtaining a new T, go (4.8) again, etc
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