Question

A platinum resistance thermometer has a resistance of 11.50 ohms at 0 oC and 17.35 ohms at 100 oC. Assuming that the resistance changes uniformly with temperature, what is the temperature when the resistance is 13.50 ohms?

Answer 1

Answer:

$34.2^{\circ}C$

Explanation:

The resistance increases linearly with the temperature - so we can write:

$\Delta R = k \Delta T$

where

$\Delta R$ is the change in resistance

k is the coefficient of proportionality

$\Delta T$ is the variation of temperature

In the first part of the problem, we have

$\Delta R = 17.35 - 11.50 =5.85\Omega$

$\Delta T = 100 -0 = 100^{\circ}C$

So the coefficient of proportionality is

$k=\frac{\Delta R}{\Delta T}=\frac{5.85}{100}=0.0585 \Omega ^{\circ}C^{-1}$

When the resistance is $R=13.50\Omega$, the change in resistance with respect to the resistance at zero degrees is

$\Delta R' = 13.50-11.50 = 2.00 \Omega$

So we can find the change in temperature as:

$\Delta T' = \frac{\Delta R}{k}=\frac{2.00}{0.0585}=34.2^{\circ}$

So the new temperature is

$T_f = T_0 + \Delta T' = 0+34.2 = 34.2^{\circ}C$