Question

Materials expand when heated. Consider a metal rod of length L0 at temperature T0. If the temperature is changed by an amount ΔT, then the rod’s length changes by ΔL=????L0ΔT, where ???? is the thermal expansion coefficient. For steel, ????=1.24×10−5∘C−1. (a) A steel rod has length L0=70cm at T0=70∘C. What is its length at T=110∘C?

Answer 1

`\Rightarrow L=70 .03472 cm`

Step-by-step explanation:

For convenience, let's represent the thermal expansion coefficient by
`\alpha`, i.e.
`????=\alpha`.

Given that, for steel
`\alpha =1.24* 10^(-5)` °
`C^(-1)`,

initial length,
`L_0=70 cm`, initial temperature,
`T_0=70` °
`C`, and the final temperature,
`T=110` °
`C`.

Let the length of the rod at
`T=110` °
`C` be
`L`.

Now, change in length,
`\Delta L=\alpha L_0 \Delta T`

`\Rightarrow \Delta L=\alpha L_0 (T-T_0)`

`\Rightarrow L-L_0=1.24* 10^(-5)* 70 (110-70)`

`\Rightarrow L-70=1.24* 10^(-5)* 70 * 40`

`\Rightarrow L=70 + 0.03472 cm`

`\Rightarrow L=70 .03472 cm`

Hence, the length of the rod at
`T=110` °
`C` be
`70.03472 cm`.