Question #8153

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 resistance and temperature. We assume that resistance changes linearly with respect to temperature, i.e.

R = αT.

Let's find coefficient α.

Difference in temperature: 100-0 = 100 C.

Difference in resistance: 52.5-9.75 = 42.75 Ohms.

Therefore,

& alpha; = 42.75/100 = 0.4275 Ohm/K.

So, the temperature corresponding to the resistance of 8.25 ohms is

T = R/α = 8.25/0.4275 ≈ 19.2982 K.

R = αT.

Let's find coefficient α.

Difference in temperature: 100-0 = 100 C.

Difference in resistance: 52.5-9.75 = 42.75 Ohms.

Therefore,

& alpha; = 42.75/100 = 0.4275 Ohm/K.

So, the temperature corresponding to the resistance of 8.25 ohms is

T = R/α = 8.25/0.4275 ≈ 19.2982 K.

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