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mws_che_inp_txt_ndd_examples

# mws_che_inp_txt_ndd_examples - Chapter 05.03 Newtons...

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05.03.1 Chapter 05.03 Newton’s Divided Difference 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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05.03.2 Chapter 05.03 Figure 1 Specific heat of water vs. temperature. Determine the value of the specific heat at C 61 T using Newton’s divided difference method of interpolation and a first order polynomial. Solution For linear interpolation, the specific heat is given by ) ( ) ( 0 1 0 T T b b T C p Since we want to find the velocity at C 61 T , and we are using a first order polynomial 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 T and 82 T . Then , 52 0 T 4186 ) ( 0 T C p , 82 1 T 4199 ) ( 1 T C p gives ) ( 0 0 T C b p 4186 0 1 0 1 1 ) ( ) ( T T T C T C b p p 52 82 4186 4199 43333 . 0
Newton’s Divided Difference Interpolation – More Examples: Chemical Engineering 05.03.3 Hence ) ( ) ( 0 1 0 T T b b T C p ), 52 ( 43333 . 0 4186 T 82 52 T At 61 T , ) 52 61 ( 43333 . 0 4186 ) 61 ( p C C kg J 9 . 4189 If we expand ), 52 ( 43333 . 0 4186 ) ( T T C p 82 52 T we get , 43333 . 0 5 . 4163 ) ( T T C p 82 52 T and this is the same expression as obtained in the direct method. Example 2 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 2.

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