Question

At 0.0 degrees Celsius, a wire cable is 410.0000 meters in length. When the temperature increased to 30.0 degrees Celsius, the wire increased in length by 0.3444 meters and measured 410.3444 meters. What is the coefficient of expansion for the wire?

Remember to include your data, equation, and work when solving this problem.

Answer 1

Answer: The coefficient of expansion for the wire
`0.000028 (^oC)^(-1)`.

Step-by-step explanation:

Original length of the wire = L= 410.0000 m

Initial temperature =
`T_1=0.0^oC`

Final Temperature =
`T_2=30.0^oC`

Increase in Length of the wire =
`\Delta L=0.3444 m`

`(\Delta L)/(L)=\alpha _(L)* \Delta T=\alpha _(L)* (T_2-T_1)`

`\alpha _L=(\Delta L)/(L* (T_2-T_1))=(0.3444 m)/(410.0000 m* (30.0^oC-0.0^oC))`

`\alpha _L=0.000028 (^oC)^(-1)`

The coefficient of expansion for the wire
`0.000028 (^oC)^(-1)`.