mws_che_inp_txt_direct_examples

mws_che_inp_txt_direct_examples - Chapter 05.02 Direct...

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05.02.1 Chapter 05.02 Direct 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 Determine the value of the specific heat at C 61 T using the direct method of interpolation and a first order polynomial.

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05.02.2 Chapter 05.02 Figure 1 Specific heat of water vs. temperature. Solution For first order polynomial interpolation (also called linear interpolation), we choose the specific heat given by  T a a T C p 1 0 Figure 2 Linear interpolation.  0 0 , y x   1 1 , y x   x f 1 x y
Direct Method of Interpolation – More Examples: Chemical Engineering 05.02.3 Since we want to find the specific heat 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 0 T and 82 1 T . Then   4186 , 52 0 0 T C T p   4199 , 82 1 1 T C T p gives   4186 52 52 1 0 a a C p   4199 82 82 1 0 a a C p Writing the equations in matrix form, we have 4199 4186 82 1 52 1 1 0 a a Solving the above two equations gives 5 . 4163 0 a 43333 . 0 1

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mws_che_inp_txt_direct_examples - Chapter 05.02 Direct...

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