You have been tasked with expanding the steam tables. The tables are used to cal

Question

You have been tasked with expanding the steam tables. The tables are used to calculate the amount of energy, work in an engine cycle. To do this the following data is given to you. T=[100, 150, 200, 250, 300, 400, 500]; Cv=[1.6958, 1.9364, 2.172, 2.46, 2.639, 3.103, 3.565]; U=[2506.7, 2582.8, 2658.1, 2733.7, 2810.4, 2967.9, 3131.6]; T is the temperature in degrees C, Cv is the specific volume in m^3/kg and U is the Internal energy in kJ/kg. Plot the Specific volume and the Internal Energy against Temperature on horizontal subplots use both a symbol and a line for plotting (different symbols for each) Verify that both are linear. Calculate the slope for all the points given of Specific volume and internal energy with respect to Temperature. Average each of the slopes Use that value to calculate the Cv and U at temperatures of 700, 800, 900 degrees C Plot them together with the previous data, making sure they have different symbols than used before

Explanation / Answer

T = [100 150 200 250 300 400 500];
Cv = [1.6958 1.9364 2.172 2.46 2.639 3.103 3.565];
U = [2506.7 2582.8 2658.1 2733.7 2810.4 2967.9 3131.6];

slopes_Cv = [];
slopes_U = [];

for i=1:size(T,2)
    if i==1
        slopes_Cv(end+1) = (Cv(2)-Cv(1))/2.0;
        slopes_U(end+1) = (U(2)-U(1))/(T(2)-T(1));
    else
        slopes_Cv(end+1) = (Cv(i)-Cv(i-1))/(T(i)-T(i-1));
        slopes_U(end+1) = (U(i)-U(i-1))/(T(i)-T(i-1));
    end
end

av_cv = mean(slopes_Cv);
fprintf('Average slope of cv: %f ', av_cv);
av_u = mean(slopes_U);
fprintf('Average slope of u: %f ', av_u);
constant_cv = (sum(Cv) - av_cv*sum(T))/size(T,2);
constant_u = (sum(U) - av_u*sum(T))/size(T,2);
Cv_700 = av_cv*700 + constant_cv;
fprintf('Cv at 700: %f ', Cv_700);
Cv_800 = av_cv*800 + constant_cv;
fprintf('Cv at 800: %f ', Cv_800);
Cv_900 = av_cv*900 + constant_cv;
fprintf('Cv at 900: %f ', Cv_900);
U_700 = av_u*700 + constant_u;
fprintf('U at 700: %f ', U_700);
U_800 = av_u*800 + constant_u;
fprintf('U at 800: %f ', U_800);
U_900 = av_u*900 + constant_u;
fprintf('U at 900: %f ', U_900);

figure
subplot(2,1,1)
hold on
plot(T, Cv, 'r*')
plot(700, Cv_700, 'r^')
plot(800, Cv_800, 'r^')
plot(900, Cv_900, 'r^')
subplot(2,1,2)
hold on
plot(T, U, 'go')
plot(700, U_700, 'd')
plot(800, U_800, 'd')
plot(900, U_900, 'd')

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