Derivative calculator with central difference formula Find the volumetric thermal expansion coefficient for each temperature given in the table. Solve BY MATLAB

Method: Derivative calculator with central difference formula

Question: The change in density of water, ρ (kg / m3), in the temperature range of 291-338 K is given in the table below. It is defined by the relation of volumetric thermal expansion coefficient of any substance. Find the volumetric thermal expansion coefficient for each temperature given in the table. Solve BY MATLAB

β = − (1/ρ ) (dρ/dT)

[darova]

I don't understand what should be found. You have to calculate β?

[darova]

Derivate of ρ can be written as:

[darova]

Use diff to calculate derivative

Answer 1

[darova]

Or maybe gradient will be better aproach here. diff returns (n-1) points

T = [291  296 305   309  311    316    322   328  331    338];
rho = [999   997    996    994   992    990   988   986   983  980];
w = -1./rho.*gradient(rho,T);
plot(T,w)