A certain material is in a room at 25°C.If the absolute temperature (K)of the material is tripled,its resistance doubles.(Water freezes at 273 K. )What is the value for α,the temperature coefficient of resistivity? A)0.020 (°C)−¹ B)0.0034 (°C)−¹ C)0.0017 (°C)−¹ D)5.96 (°C)−¹

Question

Quizplus · Accepted Answer

Let R be the resistance of the material at 25°C, and let α be the temperature coefficient of resistivity. 
When the absolute temperature of the material is tripled, it becomes 3 times 298 K = 894 K. 
According to the problem, at this temperature, the resistance becomes 2R. 
Using the formula for the temperature dependence of resistance, we have:

R(1 + αΔT) = 2R

Simplifying,

1 + αΔT = 2

αΔT = 1

α = 1/ΔT

We can use the freezing point of water as a reference temperature to calculate ΔT:

ΔT = 273 - 25 = 248 K

Therefore,

α = 1/248 ≈ 0.004

The closest choice to this value is (C) 0.0017 (°C)−1.

A Certain Material Is in a Room at 25°C