Question

Temperatures are often measured with electrical resistance thermometers. Suppose that the resistance of such a resistance thermometer is 163Ω when its temperature is 20.1∘C. The wire is then immersed in a liquid, and the resistance drops to 103Ω. The temperature coefficient of resistivity of the thermometer resistance is a =4.25×10−³(C∘)−¹. What is the temperature of the liquid? Number Units

Answer 1

The temperature of the liquid in which the resistance thermometer is immersed is approximately -19.9°C, calculated using the formula R = R0(1 + α4T), given that R0 is 163Ω at 20.1°C, R is 103Ω, and α is 4.25×10−3°C−1.

Step-by-step explanation:

The temperature of the liquid can be calculated using the formula for the temperature dependence of the resistance of an object: R = R0(1 + αΔT), where R0 is the original resistance, R is the resistance after the temperature change ΔT, and α is the temperature coefficient of resistivity.

From the given information, we have the following:

• R0 = 163Ω (resistance at temperature 20.1°C)
• R = 103Ω (resistance after immersion in liquid)
• α = 4.25×10−3°C−1 (temperature coefficient of resistivity)
• ΔT (change in temperature) = T - 20.1°C

Inserting these values into the formula we get:

1. 103 = 163(1 + 4.25×10−3ΔT)
2. 103/163 = 1 + 4.25×10−3ΔT
3. 4.25×10−3ΔT = 103/163 - 1
4. ΔT ≈ (103/163 - 1) / (4.25×10−3)
5. ΔT ≈ -40°C (rounded to the nearest whole number)

Thus, the temperature T of the liquid is approximately 20.1°C - 40°C = -19.9°C.