Q. 95.0( 2 Votes )
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.
Rθ1= Resistance at 0°C=20.0Ω
Rθ2= Resistance at 100°C=27.5Ω
Rθ3= Resistance at 420°C=50.0Ω
R0 = ?, α=?, β=?
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,
Putting R0 in eqn.2 and eqn.3, and substituting given values, we get,
Eqn.2 as , and
Now, from eqn.2 after re arranging, we get,
Putting this value in eqn. 3, we get
Putting the value of in eqn.4 , we get
Hence, the required values are
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