Question

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?

Answer 1

The temperature coefficient of resistivity is 0.001689 /°C

Step-by-step explanation:

Given initial temperature
`T_(1)`= 25°C = 25 + 273 = 298 k

The final temperature
`T_(2)` = Three times
`T_(1)` = 3

Resistance at
`T_(1)`=
`R_(1)`

Resistance at
`T_(2)` (
`R_(2)`)= double resistance at
`T_(1)` = 2
`R_(1)`

The resistance of a body can be obtained when given the above parameters with the expression below;

`R_(2) = R_(1) [1 +\alpha (T_(2)-T_(1))`...............................1

Inputting the parameters into equation 1 we have;

2
`R_(1)` =

isolating α we have;

`\alpha =(1)/(2T_(1) )`

α = 1/(2 x 298 k)

α = 1/596

α = 0.001678 /K = 0.001689 /°C (change in temperature is the same at both centigrade and kelvin scale.

Therefore the temperature coefficient of resistivity is

0.001689 /°C