Chapter 4. Heat effect-student

Chapter 4 Heat - In two circumstances = ∂ ∂ dV V U T Will be true 1 Constant volume 2 U is independent on V This is exactly true for ideal

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Unformatted text preview: In two circumstances ) ( = ∂ ∂ 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 In two circumstances ) ( = ∂ ∂ 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 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 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. ( 29 2 2 2 2 2 ) 1 ( 3 ) 1 ( 2 ) ( 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 T T ≡ τ These equations can be used to evaluate H P C With 2 2 2 ) 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, etcof this value to (4....
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This note was uploaded on 05/01/2011 for the course CHBE 2110 taught by Professor Gallivan during the Spring '08 term at Georgia Institute of Technology.

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Chapter 4 Heat - In two circumstances = ∂ ∂ dV V U T Will be true 1 Constant volume 2 U is independent on V This is exactly true for ideal

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