The resistance of the platinum wire of a platinum resistance thermometer at the ice point is 5 Ω and at the steam point is 5.23 Ω. When the thermometer is inserted in a hot bath, the resistance of the platinum wire is 5.46 Ω. Calculate the temperature of the bath.

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Accepted Answer

(2) 200°C. Given: R₀ = 5 Ω at the ice point (0°C), R₁₀₀ = 5.23 Ω at the steam point (100°C), Rₜ = 5.46 Ω in the bath. Idea: Rₜ = R₀(1 + α t), so the rise in resistance is proportional to the rise in temperature. t = (Rₜ - R₀)/(R₁₀₀ - R₀)×100°C = (5.46 - 5)/(5.23 - 5)×100°C. t = (0.46)/(0.23)×100°C = 200°C. The 0.46 Ω rise is twice the 0.23 Ω rise over 100°C, so the bath is at 200°C.

The resistance of the platinum wire of a platinum resistance thermometer at the ice point is 5 Ω and at the steam point is 5.23 Ω. When the thermometer is inserted in a hot bath, the resistance of the platinum wire is 5.46 Ω. Calculate the temperature of the bath.

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