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At 19°C, a rod is exactly 19.11 cm long on a steel ruler. Both the rod and the ruler are placed in an oven at 280°C, where the rod now measures 19.26 cm on the same ruler. What is the coefficient of thermal expansion for the material of which the rod is made? The linear expansion coefficient of steel is 11 x 10-6 1/C°?

Respuesta :

Answer:

[tex]\alpha = 4.12 \times 10^{-5} per Degree C[/tex]

Explanation:

As we know that when we increase the temperature of the rod and the ruler then in that case there will be change in the length of the both.

Due to this the ruler measurement is different from actual length of the rod

So by thermal expansion we know that

[tex]L = L_o(1 +\alpha \Delta T)[/tex]

[tex]L = 19.11 (1 + \alpha(280 - 19))[/tex]

[tex]L = 19.11(1 + 261\alpha)[/tex]

Now for length of unit division of steel scale

[tex]1 unit = 1( 1 + \alpha_s \Delta T)[/tex]

[tex]1 unit = (1 + (11 \times 10^{-6})(280 - 19))[/tex]

[tex]1 unit = 1.0029[/tex]

now the measured length from the scale is given as

[tex]L_{measured} = \frac{L}{1.0029}[/tex]

[tex]L_{measured} = \frac{19.11(1 + 261\alpha)}{1.0029}[/tex]

[tex]19.26 = \frac{19.11(1 + 261\alpha)}{1.0029}[/tex]

[tex]\alpha = 4.12 \times 10^{-5} per Degree C[/tex]

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