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# Benutzer:MichaelFrey/Pt100

${\displaystyle T=(R_{t}/100\;-1)/0,00407-(5,67\cdot 10^{-6}\cdot R_{t}^{3}-0,002498437\cdot R_{t}^{2}+0,229364156\cdot R_{t}-3,6222)}$

oder

${\displaystyle T=(R_{t}/100\;-1)/a'-(p\cdot 10^{-6}\cdot R_{t}^{3}+q\cdot R_{t}^{2}+e\cdot R_{t}+s)}$

wobei

${\displaystyle a'=4,07\cdot 10^{-3}}$
${\displaystyle p=5,67\cdot 10^{-6}}$
${\displaystyle q=-2,498437\cdot 10^{-3}}$
${\displaystyle r=229,364156\cdot 10^{-3}}$
${\displaystyle s=-3,6222}$
Gleichung
${\displaystyle T=(R_{t}/100\;-1)/a'-(p\cdot R_{t}^{3}+q\cdot R_{t}^{2}+r\cdot R_{t}+s)}$ Ausmultiplizieren von ${\displaystyle {\frac {1}{a'}}}$
${\displaystyle T={\frac {R_{t}}{100\cdot a'}}-{\frac {1}{a'}}-(p\cdot R_{t}^{3}+q\cdot R_{t}^{2}+r\cdot R_{t}+s)}$ Auflösen von ${\displaystyle -(...)}$
${\displaystyle T={\frac {R_{t}}{100\cdot a'}}-{\frac {1}{a'}}-p\cdot R_{t}^{3}-q\cdot R_{t}^{2}-r\cdot R_{t}-s}$ Sotieren von ${\displaystyle R_{t}^{3}}$ zu ${\displaystyle R_{t}^{0}(=1)}$
${\displaystyle T=-p\cdot R_{t}^{3}-q\cdot R_{t}^{2}-r\cdot R_{t}{\frac {R_{t}}{100\cdot a'}}-s-{\frac {1}{a'}}}$ Im Nächsten Schritt definieren wir neue Konstanten
${\displaystyle T=t\cdot R_{t}^{3}+u\cdot R_{t}^{2}+v\cdot R_{t}+w}$ wobei:
${\displaystyle t=-p}$
${\displaystyle u=-q}$
${\displaystyle v=r+{\frac {1}{100\cdot a'}}}$
${\displaystyle w=-s-{\frac {1}{a'}}}$
Einsetzen
${\displaystyle t=-5,67\cdot 10^{-6}}$
${\displaystyle u=2,498437\cdot 10^{-3}}$
${\displaystyle v=229,364156\cdot 10^{-3}+{\frac {1}{100\cdot 4,07\cdot 10^{-3}}}}$
${\displaystyle w=3,6222-{\frac {1}{4,07\cdot 10^{-3}}}}$
ausrechnen
${\displaystyle t=-5,67\cdot 10^{-6}}$
${\displaystyle u=2,498437\cdot 10^{-3}}$
${\displaystyle v=2,22764}$
${\displaystyle w=-242,078}$
${\displaystyle T=-5,67\cdot 10^{-6}\cdot R_{t}^{3}+0,0024984\cdot R_{t}^{2}+2,22764\cdot R_{t}-242,078}$

solve R=100*(1+3.9083*10^-3*t-5.775*10^-7*t*t-4.183*10^-12*(T-100)*t*t*t), t