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

Answer:

100.11 m

Explanation:

Given:

Coefficient of volume expansion, $\alpha_{v}=33\times10^{-6}$ /°C.

Initial length of rod, $l=100 m$

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

We know that,

$\alpha_{v}=3\alpha_{L}\\\alpha_{L}=\frac{\alpha_{v}}{3}\\\alpha_{L}=\frac{33\times10^{-6}}{3}=11\times10^{-6}$ /°C

Here, $\alpha_{L}$ is the coefficient of linear expansion.

Now, we know that,

Change in length (Δl) is given as,

$\Delta l=\alpha_L\times L\times\Delta T$

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

This gives,

$\Delta l=11\times10^{-6}\times 100\times100\\\Delta l=0.11 \textrm{ m}$

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