Question

A steel cable spanning a river is 298 .000 m long when the temperature is 20 .0

Answer 1

Delta L = L(initial) * alpha * delta t

Delta L = 298 * 12* (10^-6) * -26

= -0.092976 m

L = L(initial) + delta L

=298 -0.092976

L(final) = 297.907 m

Answer 2

apply alpha = L2-L1/( L1 * (T2-T1)

so L2 = L1(1+ alpha (T2-T1)

L2 = 298 *(1+ 0.000012 * 26)

L2 = 297.907

Answer 3

Change in length would be 12.

Answer 4

L_f = L_i + coefficient of thermal expansion*(T_f - T_i )

L_f = 298 + 12*10^-6*(-6-20) = 297.999m (To six significant digits)