How to define a variable as a condition of other variables

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.

[Cris LaPierre]

What have you tried so far? You'll find the community happy to help you fix your code, but more hesitant to code your assignment for you.

[Madison Cocker]

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'.

Answer 1

[Torsten]

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.

Answer 2

[David Hill]

TSI=1000:2000;
T=(TSI/r^2/SB_constant*L^2).^.25;

Answer 3

[Enrico Gambini]

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