# 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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