1) It means that the ratio [tex]\frac{\Delta L}{L}[/tex], where [tex]\Delta L[/tex] is the change in length of the material and L is the original length, change by 0.000017 units for an increase in temperature of 1 Kelvin.
2) The safety gap between two successive bars is 0.33 mm
Explanation:
1)
When a solid material is heated and its temperature increases, the material expands. The linear expansivity of the material gives a measure of how much the length of the material increases per unit temperature change.
For instance, the linear expansivity of copper is
[tex]\alpha = 0.000017/K[/tex]
which means that the ratio [tex]\frac{\Delta L}{L}[/tex], where [tex]\Delta L[/tex] is the change in length of the material and L is the original length, change by 0.000017 units for an increase in temperature of 1 Kelvin.
In formula, this can be rewritten as
[tex]\frac{\Delta L}{L} = \alpha \Delta T[/tex]
where [tex]\Delta T[/tex] is the change in temperature of the material.
2)
To solve this part of the problem, we can use the formula given in the previous part:
[tex]\frac{\Delta L}{L} = \alpha \Delta T[/tex]
Which can be rewritten as
[tex]\Delta L =L \alpha \Delta T[/tex]
where in this case, we have:
L = 3 m is the original length of the steel bar
[tex]\alpha = 1.0\cdot 10^{-5} /K[/tex] is the linear expansivity of steel
[tex]\Delta T = 40^{\circ}C-29^{\circ}C=11^{\circ}C[/tex] is the increase in temperature of the steel bar
Therefore, by solving the formula for [tex]\Delta L[/tex], we find the increase in length of the steel bars when the temperature increases to 40 degrees:
[tex]\Delta L = (3)(1.0\cdot 10^{-5})(11)=3.3\cdot 10^{-4} m = 0.33 mm[/tex]
This means that the safety gap between two successive bars must be 0.33 mm.
Learn more about temperature:
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