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mws_che_inp_txt_spline_examples

# mws_che_inp_txt_spline_examples - Chapter 05.05 Spline...

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05.05.1 Chapter 05.05 Spline Method of 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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05.05.2 Chapter 05.05 Figure 1 Specific heat of water vs. temperature. Determine the value of the specific heat at C 61 T using linear splines. Solution Since we want to find the specific heat at C 61 T and we are using linear splines, we need to choose the two data points 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 , 52 0 T 4186 ) ( 0 T C p , 82 1 T 4199 ) ( 1 T C p gives ) ( ) ( ) ( ) ( ) ( 0 0 1 0 1 0 T T T T T C T C T C T C p p p p ) 52 ( 52 82 4186 4199 4186 T Hence 82 52 ), 52 ( 43333 . 0 4186 ) ( T T T C p At , 61 T ) 52 61 ( 43333 . 0 4186 ) 61 ( p C
Spline Method of Interpolation-More Examples: Chemical Engineering 05.05.3 C kg J 9 . 4189 Linear spline interpolation is no different from linear polynomial interpolation. Linear splines still use data only from the two consecutive data points. Also at the interior points of the data, the slope changes abruptly. This means that the first derivative is not continuous at these points. So how do we improve on this? We can do so by using quadratic splines.

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mws_che_inp_txt_spline_examples - Chapter 05.05 Spline...

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