A certain material is in a room at 27 $\degree$C.If the absolute temperature (K)of the material is tripled,its resistance doubles.(Water freezes at 273 K. )What is the value for a,the temperature coefficient of resistivity? A)1 ( $\degree$C)^-1 B)2 ( $\degree$C)^-1 C)0.001 7 ( $\degree$C)^-1 D)0.038 ( $\degree$C)^-1

Question

Quizplus · Accepted Answer

Let's first convert the temperature given in Fahrenheit to Kelvin:

T = (27°F + 459.67) × 5/9 = 269 K

When the absolute temperature is tripled, it becomes:

T' = 3T = 807 K

If the resistance doubles, then the temperature coefficient of resistivity a can be calculated using the formula:

a = (ln 2) / ((T'/T) - 1)

a = (ln 2) / ((807 K / 269 K) - 1) = 0.0017 (°C)^-1

However, the answer choices are given in (°F)^-1, so we need to convert:

0.0017 (°C)^-1 * (9/5)^-1 = 0.00094 (°F)^-1

The closest answer choice is C, 0.0017 (°C)^-1 or 0.00094 (°F)^-1.

A Certain Material Is in a Room at 27 °\degree° CIf the Absolute Temperature (K)of the Material Is Tripled,its Resistance

A Certain Material Is in a Room at 27 $\degree$ CIf the Absolute Temperature (K)of the Material Is Tripled,its Resistance