Question

A rod made up of certaon metall which had coefficiebt of volume expansion is 33×10^-6 per celsius degrer.The rod is 100 meter long and then it is heated from -10°c to 90°c. The length of rod is

Answer 1

100.11 m

Step-by-step explanation:

Given:

Coefficient of volume expansion,
`\alpha_(v)=33*10^(-6)` /°C.

Initial length of rod,
`l=100 m`

Change in temperature, ΔT=
`(90-(-10))=100` °C

We know that,

`\alpha_(v)=3\alpha_(L)\\\alpha_(L)=(\alpha_(v))/(3)\\\alpha_(L)=(33*10^(-6))/(3)=11*10^(-6)` /°C

Here,
`\alpha_(L)` is the coefficient of linear expansion.

Now, we know that,

Change in length (Δl) is given as,

`\Delta l=\alpha_L* L*\Delta T`

Plug in all the values and solve for
`l`.

This gives,

`\Delta l=11*10^(-6)* 100*100\\\Delta l=0.11 \textrm{ m}`

Therefore, the length of rod after expansion is
`L+\Delta l=100+0.11=100.11` m.