A certain material is in a room at 27°C. If the absolute temperature (K) of the material is tripled, its resistance quadruples. (Water freezes at 273 K.) What is the value for $\alpha$, the temperature coefficient of resistivity? A) 0.0050 (°C) ^- ¹ B) 0.0025 (°C) ^- ¹ C) 1 (°C) ^- ¹ D) 3 (°C) ^- ¹

Question

Quizplus · Accepted Answer

The temperature coefficient of resistivity is given by:$$\alpha = \frac{1}{R}\frac{dR}{dT}$$where R is the resistance and T is the temperature.In this problem, the resistance quadruples when the absolute temperature triples. Therefore, we have:$$\frac{R_2}{R_1} = 4$$and$$\frac{T_2}{T_1} = 3$$Substituting these values into the equation for the temperature coefficient of resistivity, we get:$$\alpha = \frac{1}{4}\frac{dR}{dT} = \frac{1}{4}\frac{R_2 - R_1}{T_2 - T_1} = \frac{1}{4}\frac{3R_1}{2T_1} = \frac{3}{8}\frac{R_1}{T_1}$$Since the material is at 27°C, we have:$$T_1 = 27°C + 273 K = 300 K$$Substituting this value into the equation for the temperature coefficient of resistivity, we get:$$\alpha = \frac{3}{8}\frac{R_1}{T_1} = \frac{3}{8}\frac{R_1}{300 K} = 0.0025 (°C)^{-1}$$Therefore, the correct answer is B.

A Certain Material Is in a Room at 27°C α\alphaα , the Temperature Coefficient of Resistivity? A) 0

A Certain Material Is in a Room at 27°C $\alpha$ , the Temperature Coefficient of Resistivity?
A) 0