Question

The length L (in centimetre) of a copper rod is a linear function of its Celsius temperature C. In an experiment, if L = 124.942 when C = 20 and L = 125.134 when C = 110, express L in terms of C.

Answer 1

The length L ( cm ) of a copper rod is the linear function of its temperature C ( celcius ) .

Suppose temperature is plotted along x axis and length is plotted along the y- axis.

It is given that when temperature

The coordinates of the points through which the straight line passes are ( 20,124.942 ) and ( 110,125.134 ) .

Now, the formula for the equation of line passing through the points ( x 1 , y 1 ) and ( x 2 , y 2 ) is given by,

( y− y 1 )= y 2 − y 1 x 2 − x 1 ⋅( x− x 1 ) (1)

Substitute ( x 1 , y 1 ) as ( 20,124.942 ) and ( x 2 , y 2 ) as ( 110,125.134 ) in equation (1).

( y−124.942 )= 125.134−124.942 110−20 ⋅( x−20 ) ( y−124.942 )= 0.192 90 ⋅( x−20 ) y= 0.192 90 ⋅( x−20 )+124.942

The y coordinate represents length L ( cm ) and x coordinate represents temperature; above equation could be rewritten as

L= 0.192 90 ⋅( C−20 )+124.942

The expression of length L ( cm ) in terms of temperature C ( celcius ) is L= 0.192 90 ⋅( C−20 )+124.942 .