Question #8176

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.

Expert's answer

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.

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.

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