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

Temperature = 34.19 °C

Step-by-step explanation:

At temperature T₁ = 0 °C

Resistance R₁ = 11.50 Ohms

At Temperature T₂ = 100 °C

Resistance R₂ = 17.35 Ohms

The change in resistance = ΔR = R₂ - R₁

ΔR = 17.35 - 11.50 = 5.85 Ω

The change in Temperature = ΔT = T₂ - T₁

ΔT = 100 - 0 = 100 °C

Temperature coefficient of resistance = α = ΔR / ΔT

Temperature coefficient of resistance is the measure of change in electrical resistance of any substance per degree change in temperature.

α = 5.85 / 100 = 0.0585 Ω / °C

We need to find the temperature when resistance is 13.50 Ω

So,

Temperature = T = ?

Resistance = R = 13.5 Ω

The change from 2.71Ω to 3.26Ω = 13.5 - 11.5 = 2.00 Ω

The temperature Change required is = 2.00 / 0.0585 = 34.19 °C

Temperature = T = 0 + 34.19 = 34.19 °C

At Temperature 34.19 °C the Resistance will be 3.26 Ω