Samyak Jain
Last Activity: 5 Years ago
Take a small element dx of the road at a distance x from one end and we need to find change in length dL of this element for temperature change
T = (20 – 0)
C = 20
C
But first we need expansion coefficient for this element which is by definition
the fractional change in length per unit change in temperature.
i.e.
= dL / dx
T = (3x + 2).10
– 6i.e. dL = (3x + 2).10
– 6 dx
T , here
T is constant.
Integrating both sides, we get
L =
T.10
– 6 (3 x
2 / 2 + 2 x) with limits of x from 0 to 200 cm.
L =
T.10
– 6 (3.200
2 / 2 + 2 x 200) =
T.10
– 6 (60000 + 400) = 604 x 10
– 4 T
= 604 x 10 – 4 x 20 = 1.208 cm
But
L = L – 200 cm , where L is the final length of road at 20
C.
So, L – 200 cm = 1.208 cm
L = 201.208 cm.
