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

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Abdulaziz Muslem 2021-6-1

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编辑： Abdulaziz Muslem 2023-5-26

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)

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darova 2021-6-1

Derivate of ρ can be written as:

darova 2021-6-1

Use diff to calculate derivative

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darova 2021-6-1

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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)

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