The wire of a platinum resistance thermometer has d resistance of 3.5 at 0 °C and 10.52 at 100°C. Calculate…

Analyze the question: A platinum resistance thermometer measures temperature through the change in resistance of the wire. We are given the resistance at the two fixed points (0 °C and 100 °C) and asked for the temperature at which R = 7.5 Ω.

Concept: Assuming resistance varies linearly with temperature:

θ = [(R_θ − R₀) / (R₁₀₀ − R₀)] × 100 °C

Solution:

• R₀ = 3.5 Ω
• R₁₀₀ = 10.52 Ω
• R_θ = 7.5 Ω

θ = [(7.5 − 3.5) / (10.52 − 3.5)] × 100

θ = (4.0 / 7.02) × 100

θ = 0.5698 × 100 ≈ 56.98 °C ≈ 57 °C

Answer: D. 57 °C

Tip: For resistance thermometer questions, remember the pattern "(value − lower fixed point) ÷ (upper fixed point − lower fixed point) × 100." The same formula works for any thermometer with a linear property (e.g. mercury length or gas pressure). Quick check: 7.5 is a little over halfway between 3.5 and 10.52 (midpoint ≈ 7.01), so the answer should be a bit above 50 °C. That is consistent with 57 °C.