A thermistor's resistance follows R(T) = R_0 ,e^ B ( 1 T - 1 T_0 )

PHYSICS · Subjective · Fermi University Physics · Computational Physics · Scientific programming for physicists · Scientific programming for physicists

Computational Physics, Ch Letting the computer do the algebra

Problem

A thermistor's resistance follows

R(T) = R_0\,e^{B\left(\frac{1}{T}-\frac{1}{T_0}\right)},

where

R_0 = 10.0\,\mathrm{k\Omega}

is the resistance at reference temperature

T_0=298\,\mathrm{K}

B=3900\,\mathrm{K}

is a material constant, and

T

is the absolute temperature in kelvin. (a) Enter

R(T)

as a symbolic expression in the single symbol

T

, with

R_0

B

and

T_0

already substituted as numbers, and convert it into a numerical function of a NumPy array of temperatures using lambdify. (b) Evaluate the compiled function at

T = 280, 290, 298, 310, 320\,\mathrm{K}

and give each resistance to three significant figures, in

\mathrm{k\Omega}

. (c) Check the value at

T=298\,\mathrm{K}

by substituting directly into the original symbolic expression and evaluating it numerically. State whether the two routes agree to machine precision, and explain why that agreement is expected even though the derivation involved no approximation at any stage.

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