Question

A steel cable spanning a river is 200,000 m long when the temperature is 20.^oC. What will be its length when the temperature drops to 0^oC? (The coefficient of thermal expansion of steel is 12.x10^-6K^-1.)

Answer 1

Here ,

initial length , Lo = 200,000 m

change in temperature , del T = 20 degree C

thermal expansion coefficient , alpha = 1.2 *10^-6 K^-1

Now , for the length at T = 0 degree C

length = Lo *(1 - alpha * delta T)

length = 200000 * ( 1 - 1.2 *10^-6 * 20)

length = 199995.2 m

the length of the cable at 0 degree C is 199995.2 m