Question

A metal rod 45.0000-cm long at 55.0 °C is heated to 86.0 °C. The length of the rod is then measured to be 45.0364 cm. What is the coefficient of linear expansion of the metal?

Answer 1

Answer:

check the attachment attached

Answer 2

Answer:

The coefficient of linear expansion of the metal is $2.5\times 10^-^5/\textdegree C$.

Explanation:

We will use the following the relation to solve this question,

$L=L_0(1+\alpha \Delta T)$     (1)

Where,

L=final length of the rod

L₀=initial length of the rod

α=coefficient of linear expansion

ΔT=change in temperature

From the question we have,

L₀=45.0000cm

L=45.0364 cm

T₁=55.0 °C

T₂=86.0 °C

So,

$\Delta T=T_2-T_1$   (2)

By substituting the values in equation (2) we get;

$\Delta T=86.0\textdegree C-55.0\textdegree C=31\textdegree C$   (3)

By substituting the required values in equation (1) we get;

$45.0364=45.0000(1+\alpha \times 31)$

$1.0008=1+\alpha\times 31$

$\alpha=\frac{8\times 10^-^4}{31}$

$\alpha=2.5\times 10^-^5/\textdegree C$

Hence, the coefficient of linear expansion of the metal is $2.5\times 10^-^5/\textdegree C$.