Find the temperature range of 25m aluminum cable that contact and expands by 7mm for each day
Answers
Answer:
Change in length is related to original length, the type of material and the amount of temperature change.
The formula for linear expansion is
Δ
L
=
α
L
o
Δ
T
where
Δ
L
is the change in length of the object, in meters
α
is the coefficient for linear expansion of the material in question, in
^
o
C
−
1
L
o
is the original length of the object, in meters
Δ
T
is the change in temperature, in Kelvin (or degrees Celsius)
The coefficient for linear expansion for the material can be referenced from a chart in your textbook or on the Internet.
For example: The longest steel arch bridge in the US is 517 m long. If this bridge undergoes a temperature change from
−
25.0
o
C
in the winter to
45.0
o
C
in the summer, how much will it expand?
(Let us use only the coefficient of linear expansion for steel, to simplify this question.)
Δ
L
=
α
L
o
Δ
T
Δ
L
=
(
24
x
10
−
6
)
(
517
)
(
70
)
Δ
L
=
0.86586
m