Answer to Question #254016 in Calculus for Shabo

Question

In the temperature range between 0 0C and 7000C the resistance R [in ohms] of a certain platinum resistance thermometer is given by R = 10 + 0.04124T à ¢ ˆ ’ 1.779 à ƒ — 10à ¢ ˆ ’5à °  ‘ ‡ 2 where T is the temperature in degrees Celsius. Where in the interval from 0 0C to 7000C is the resistance of the thermometer most sensitive and least sensitive to temperature changes? [Hint: Consider the size of dR/dT in the interval 0 à ¢ ‰ ¤ T à ¢ ‰ ¤ 700

Answer 1

$$R=10+0.04124T-1.779\times 10^{-5}T^2$$

$$\dfrac{dR}{dT}=0.04124-3.558\times10^{-5}T$$

The function $\dfrac{dR}{dT}$ decreases for $T\in[0\degree C, 700\degree C].$

$$\dfrac{dR}{dT}|_{T=0\degree C}=0.04124\ \Omega /\degree C$$

$$\dfrac{dR}{dT}|_{T=700\degree C}=0.016334\ \Omega /\degree C$$

The resistance is most sensitive to temperature changes at $T=0\degree C,$ least sensitive at $T=700\degree C.$