How to define a variable as a condition of other variables

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Hi there, I am working on a project for an environmental science class where I need to plot the change in temperature as a function of the change in the solar constant from 1000wm-2 to 2000wm-2. The equation I need to use is TSI=r^2*Stefan-Boltzmann constnat*T^4 / L^2, where I know the values of r, SB constant, and L, but I'm not sure how to write the program such that it calculates a new temperature for each TSI value between 1000-2000, if that makes sense. I have an intial condition for the temperature as well. I assume I need a for loop somewhere, but I'm not sure how to start writing the equation for finding each temperature.
Thanks very much.
  2 Comments
Madison Cocker
Madison Cocker on 16 Mar 2022
Hi There, thank you for your response. I defined all my variables like so, and when I attempted to define T and TSI was where my problem arose because they are functions of each other. I hope that helps
L=1.5*10^11
r=6.95*10^8
SB=5.67*10^-8
>> TSI=(r.^2 .* SB .*T.^4)/L.^2
Unrecognized function or variable 'T'.
>> T=TSI/SB
Unrecognized function or variable 'TSI'.

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Accepted Answer

Torsten
Torsten on 16 Mar 2022
Edited: Torsten on 16 Mar 2022
dTSI = r^2*SBC*4*T^3*dT/L^2
dT = dTSI*L^2/(r^2*SBC*4*T^3)
dT/dTSI = L^2/(r^2*SBC*4*T^3)
Thus in MATLAB:
r = ...;
SBC = ...;
L = ...;
TSI = 1000:1:2000;
T = (TSI*L^2/(r^2*SBC)).^0.25
dTdTSI = L^2./(r^2*SBC*4*T.^3)
plot(TSI,dTdTSI)
I'm still not 100% certain if this is really what you are told to plot, but I guess it's correct.

More Answers (2)

David Hill
David Hill on 16 Mar 2022
TSI=1000:2000;
T=(TSI/r^2/SB_constant*L^2).^.25;

Enrico Gambini
Enrico Gambini on 16 Mar 2022
Edited: Enrico Gambini on 16 Mar 2022
Hi.
Generally matlab "doesn't like" for loops like other programming languages. That's because in most of the cases there is the possibility to indicize an array in a simpler (and faster) way.
Hence, for your specific problem I propose:
r=input("Insert the value of r:\n");
L=input("Insert the value of L:\n");
Sb_const=input("Insert the value of Stefann-Boltzmann constant :\n");
TSI=[1000:2000];
T=(TSI*L^2/(r^2*Sb_const)).^(1/4); %I inverted the formula and it is computing the Temperature at an interval of 1 W/m2 between 1000 and 2000
plot(TSI,T); %plot TSI vs T

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