Question

A metal rod has length 5.265 m, at 23°c.
Find the temperature at which the length of
the rod increases to 5,272 m (@= 1.3*10-5,’c loc 4​

Answer 1

Answer:

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Explanation:

A metal rod has length 5.265 m, at 23°c.

Find the temperature at which the length of

the rod increases to 5,272 m (@= 1.3*10-5,’c loc 4hiicjgcjccdickdci

Answer 2

Answer: The temperature at which the length of the rod increases is 125°C.

Explanation:

We will use the following formula to solve this question,

$\Delta L=L\alpha\Delta T$         (1)

Where,

ΔL=change in the length of the metal rod

L=initial length of the rod

α=coefficient of linear expansion of the metal

From the question we have,

l₁=5.265m

l₂=5.272m

α=1.3×10⁻⁵/°C

T₁=23°C

$\Delta L=5.272-5.265=0.007$

$\Delta L=7\times 10^-^3$    (2)

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

$7\times 10^-^3=5.265\times 1.3\times 10^-^5\times \Delta T$

$\Delta T=\frac{7\times 10^-^3}{5.265\times 1.3\times 10^-^5}$

$\Delta T=1.02\times 10^2$

$\Delta T=102\textdegree C$       (3)

Also,

$\Delta T=T_2-T_1$        (4)

By substituting the required values in equation (4) we get;

$102\textdegree C=T_2-23\textdegree C$

$T_2=125\textdegree C$

Hence, the temperature at which the length of the rod increases is 125°C.