A resistance thermometer reads R = 20.0Ω, 27.5Ω, and 50.0Ω at the ice point (0°C), the steam point (100°C) and the zinc point (420°C) respectively. Assuming that the resistance varies with temperature as Rθ = Rθ (I + αθ + βθ2), find the values of Rθ, α and β. Here θ represents the temperature on the Celsius scale.


Explanation:


Given:


Rθ1= Resistance at 0°C=20.0Ω


Rθ2= Resistance at 100°C=27.5Ω


Rθ3= Resistance at 420°C=50.0Ω


R0 = ?, α=?, β=?


Formula used



The values for 3 resistance ( are given at 3 temperatures (,


So, at temperature 0° C,


, (eqn. 1)


At 100° C,


, (eqn. 2)


At 420° C,


, (eqn. 1)


Solving this three equation simultaneously for three unknowns,


From eqn. 1, we get,


(Ans.)


Putting R0 in eqn.2 and eqn.3, and substituting given values, we get,


Eqn.2 as , and


Eqn.3 as


Now, from eqn.2 after re arranging, we get,


, (eqn.4)


Putting this value in eqn. 3, we get



Or,



Or,


(Ans.)


Putting the value of in eqn.4 , we get



(Ans.)


Hence, the required values are


(Ans.)


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