Answer to Question #8176 in Molecular Physics | Thermodynamics for Frank Omorogbe

Question

A platinium resistance thermometer has resistance of 52.5 ohms and 9.75 ohms at 0 degrees Celsius and 100 degrees Celsius respectively. When the resistance is 8.25 ohms, find the temperature.

Answer 1

Let's find out the relation between termometer resistance and temperature. We assume that resistance changes linearly with respect to temperature, i.e.
R = αT + C.
We know that
52.5 = 0α + C ==> C = 52.5
and
9.75 = 100α + C ==> α = (9.75 - C)/100 = α = (9.75 - 52.5)/100 = -0.4275.
So, the resistance of 8.25 ohms corresponds to the temperature of
T = (R - C)/α = (8.25 - 52.5)/(-0.4275) = 103.5088°C.