A platinum resistance thermometer has a resistance 4\(\Omega\) at 0oC and 10\(\Omega\) at 100oC. Assuming the resistance changes uniformly with temperature....

Answer Details

The resistance of a platinum resistance thermometer changes uniformly with temperature. Let's use the formula for the resistance-temperature relationship of a platinum resistance thermometer: R = R₀(1 + αT) Where R is the resistance at a given temperature T, R₀ is the resistance at 0°C (4Ω in this case), and α is the temperature coefficient of resistance of platinum. We can find α by using the resistance values at two different temperatures, say 0°C and 100°C: α = (R₁ - R₀) / (R₀ × ΔT) Where ΔT is the temperature difference between the two resistance values (100°C - 0°C = 100°C), and R₁ is the resistance at the higher temperature (10Ω in this case). α = (10Ω - 4Ω) / (4Ω × 100°C) = 0.015Ω/°C Now we can use the formula to find the resistance at 45°C: R = R₀(1 + αT) = 4Ω(1 + 0.015Ω/°C × 45°C) ≈ 6.7Ω Therefore, the answer is 6.7Ω.