mws_che_inp_txt_lagrange_examples

mws_che_inp_txt_lagrange_examples - Chapter 05.04...

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05.04.1 Chapter 05.04 Lagrangian Interpolation – More Examples Chemical Engineering Example 1 To find how much heat is required to bring a kettle of water to its boiling point, you are asked to calculate the specific heat of water at C 61 . The specific heat of water is given as a function of time in Table 1. Table 1 Specific heat of water as a function of temperature. Temperature, T   C Specific heat, p C C kg J 22 42 52 82 100 4181 4179 4186 4199 4217
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05.04.2 Chapter 05.04 Figure 1 Specific heat of water vs. temperature. Determine the value of the specific heat at C 61 T using a first order Lagrange polynomial. Solution For first order Lagrange polynomial interpolation (also called linear interpolation), the specific heat is given by 1 0 ) ( ) ( ) ( i i p i p T C T L T C ) ( ) ( ) ( ) ( 1 1 0 0 T C T L T C T L p p
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Lagrangian Interpolation-More Examples: Civil Engineering 05.03.3 Figure 2 Linear interpolation. Since we want the velocity at C 61 T , we need to choose the two data points that are closest to C 61 T that also bracket C 61 T to evaluate it. The two points are 52 0 T and 82 1 T . Then   4186 , 52 0 0 T C T p  4199 , 82 1 1 T C T p gives 1 0 0 0 0 ) ( j j j j T T T T T L 1 0 1 T T T T 1 1 0 1 1 ) ( j j j j T T T T T L 0 1 0 T T T T Hence ) ( ) ( ) ( 1 0 1 0 0 1 0 1 T C T T T T T C T T T T T C p p p 82 52 ), 4199 ( 52 82 52 ) 4186 ( 82 52 82 T T T ) 4199 ( 52 82 52 61 ) 4186 ( 82 52 82 61 ) 61 ( p C ( x 0 , y 0 ) ( x 1 , y 1 ) f 1 ( x ) x y
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05.04.4 Chapter 05.04 ) 4199 ( 3 . 0 ) 4186 ( 7 . 0 C kg J 9 . 4189 You can see that 7 . 0 ) ( 0 T L and 3 . 0 ) ( 1 T L are like weightages given to the specific heats at 52 T and 82 T to calculate the specific heat at 61 T . Example 2
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mws_che_inp_txt_lagrange_examples - Chapter 05.04...

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