Determine linear system of equations

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The following assignment should be solved using MATLAB.

Table 1 gives the values of the heat capacity, CP, for four gases at three different temperatures. CP is in Joules/(g mol)(°C) and T is in °C.

Table 1: Ideal gas heat capacity coefficients for four gases at three temperatures

Temperature [°C]

SO2

SO3

O2

N2

25

39.87

50.74

29.39

29.05

150

44.10

60.47

30.70

29.19

300

48.06

69.25

32.06

29.07

      The heat capacity of an ideal mixture of four gases, CPmixture, can be expressed in terms of the heat capacity of the components by the mixture equation:

                                                 CPmixture = x1CP1+x2CP2+x3CP3+x4CP4                                      (1)

where x1, x2,x3, andx4 are the fraction of the components, and CP1, CP2, CP3, and CP4 are the corresponding heat capacities. A mixture of unknown quantities of the four gases, SO2,SO3,O2,and N2, has been provided to our laboratory. In order to determine the fraction of the components in the gas mixture, use Table 2, which has the values of the heat capacity of the mixture were measured at three temperatures

Table 2: Heat capacity of the four-gas mixture at different temperatures

Temperature [°C]

25

150

300

CPmixture[Joules/(g mol)(°C)]

39.82

44.72

49.10

Use the data in Tables 1 and 2andEquation (1) to write three equations for the mixture at the three temperatures. The fourth equation is: x1+x2+x3+x4=1. Determine x1, x2,x3, andx4 by solving the linear system of equations (four equations + four unknowns).

Save all of the commands necessary to do the calculation into a script (.m) file. Annotate the .m file with sufficient comments so that we can follow the calculation and use the dispand fprintfcommands to ensure that the output to the command window is clean, neat, and able to be followed.

      Assignment is due on Friday, March 4, 2016 by midnight. Upload the script file to eCampus.

Reference no: EM13993331

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