The resistance r of a piece of wire has thermometric properties which can be described as a linear function of temperature (t), see below: where a and b are constants. the resistance of the wire is found to be 3.3 2 at the temperature of melting ice (0 °c) and 8.5 2 at the boiling of water (100 °c) at atmospheric pressure. [15 marks] a, find a and b b. determine the temperature when r is 6.9 2

Explanation:

R = a T + b ( R is linear function of T , the temperature in kelvin )

At T =  273 K , R = 3.32

Put these values in the equation above '

3.32 = 273 a + b

At 100° = 373K , R = 8.52

8.52 = 373 a + b

8.52 - 3.32 = (373 - 273 )a

a =5.2 / 100 = .052

Putting this value of a in the first equation we get the value of b as follows

3.32 = 273 x .052 + b

b = -10.876.

So equation becomes

R = .052 T - 10.876

When R = 6.92 , T =?

6.92 = .052 T -10.876

.052T = 17.796

T = 342.23K

T = 342.23 - 273 = 69.23 °C