When the temperature of a rod is changed, the length of the rod would change. This is called the linear expansion. The expansion depends on the material, the change in temperature, and the change in length of the rod. Quantitatively, the change in length can be expressed as: AL=aLAT where a is the coefficient of linear expansion, L is the original length of the rod, and AT=Tr-T, is the change in temperature. The coefficient of linear expansion can be measured by measuring the original length of the rod, the changes in length AL and the change in temperature AT. Write an expression for calculating a in terms of the original length L, the change in length AL, the initial and the final temperature of the rod. In this lab, the change in length AL will be measured by the movement of a pointer. AL is proportional to the movement e. AL = e/10. If the uncertainty in measuring e is de, then what is the expression of the relative uncertainty in AL? (Hint: there is no uncertainty in 10.) (AL)/(AL) = a = The temperature difference is AT=Tr-T₁. If the uncertainty in measuring each temperature is ST, write an expression for the absolute uncertainty in 4T. 8(AT)=
When the temperature of a rod is changed, the length of the rod would change. This is called the linear expansion. The expansion depends on the material, the change in temperature, and the change in length of the rod. Quantitatively, the change in length can be expressed as: AL=aLAT where a is the coefficient of linear expansion, L is the original length of the rod, and AT=Tr-T, is the change in temperature. The coefficient of linear expansion can be measured by measuring the original length of the rod, the changes in length AL and the change in temperature AT. Write an expression for calculating a in terms of the original length L, the change in length AL, the initial and the final temperature of the rod. In this lab, the change in length AL will be measured by the movement of a pointer. AL is proportional to the movement e. AL = e/10. If the uncertainty in measuring e is de, then what is the expression of the relative uncertainty in AL? (Hint: there is no uncertainty in 10.) (AL)/(AL) = a = The temperature difference is AT=Tr-T₁. If the uncertainty in measuring each temperature is ST, write an expression for the absolute uncertainty in 4T. 8(AT)=
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Chapter1: Units, Trigonometry. And Vectors
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Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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![**Pre-lab: Coefficient of Linear Expansion**
When the temperature of a rod is changed, the length of the rod would change. This is called linear expansion. The expansion depends on the material, the change in temperature, and the change in length of the rod. Quantitatively, the change in length can be expressed as:
\[
\Delta L = \alpha L \Delta T
\]
where \( \alpha \) is the coefficient of linear expansion, \( L \) is the original length of the rod, and \( \Delta T = T_f - T_i \) is the change in temperature.
The coefficient of linear expansion can be measured by measuring the original length of the rod, the changes in length \( \Delta L \) and the change in temperature \( \Delta T \). Write an expression for calculating \( \alpha \) in terms of the original length \( L \), the change in length \( \Delta L \), and the initial and final temperature of the rod.
\[
\alpha =
\]
In this lab, the change in length \( \Delta L \) will be measured by the movement of a pointer. \( \Delta L \) is proportional to the movement \( e \). \( \Delta L = e/10 \). If the uncertainty in measuring \( e \) is \( \delta e \), then what is the expression of the relative uncertainty in \( \Delta L \)? (Hint: there is no uncertainty in 10.)
\[
\delta(\Delta L)/(\Delta L) =
\]
The temperature difference is \( \Delta T = T_f - T_i \). If the uncertainty in measuring each temperature is \( \delta T \), write an expression for the absolute uncertainty in \( \Delta T \).
\[
\delta(\Delta T) =
\]
The relative uncertainty in \( \Delta T \) is
\[
\delta(\Delta T)/(\Delta T) =
\]
The coefficient of linear expansion can be calculated by using
\[
\alpha = \frac{e/10}{L(T_f - T_i)} = \frac{\Delta L}{L \Delta T}
\]
If the uncertainty in the original length is \( \delta L \), write an expression for calculating the uncertainty in \( \alpha \).
\[
\delta \alpha/\alpha =
\]
\[
\delta \alpha =
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Transcribed Image Text:**Pre-lab: Coefficient of Linear Expansion**
When the temperature of a rod is changed, the length of the rod would change. This is called linear expansion. The expansion depends on the material, the change in temperature, and the change in length of the rod. Quantitatively, the change in length can be expressed as:
\[
\Delta L = \alpha L \Delta T
\]
where \( \alpha \) is the coefficient of linear expansion, \( L \) is the original length of the rod, and \( \Delta T = T_f - T_i \) is the change in temperature.
The coefficient of linear expansion can be measured by measuring the original length of the rod, the changes in length \( \Delta L \) and the change in temperature \( \Delta T \). Write an expression for calculating \( \alpha \) in terms of the original length \( L \), the change in length \( \Delta L \), and the initial and final temperature of the rod.
\[
\alpha =
\]
In this lab, the change in length \( \Delta L \) will be measured by the movement of a pointer. \( \Delta L \) is proportional to the movement \( e \). \( \Delta L = e/10 \). If the uncertainty in measuring \( e \) is \( \delta e \), then what is the expression of the relative uncertainty in \( \Delta L \)? (Hint: there is no uncertainty in 10.)
\[
\delta(\Delta L)/(\Delta L) =
\]
The temperature difference is \( \Delta T = T_f - T_i \). If the uncertainty in measuring each temperature is \( \delta T \), write an expression for the absolute uncertainty in \( \Delta T \).
\[
\delta(\Delta T) =
\]
The relative uncertainty in \( \Delta T \) is
\[
\delta(\Delta T)/(\Delta T) =
\]
The coefficient of linear expansion can be calculated by using
\[
\alpha = \frac{e/10}{L(T_f - T_i)} = \frac{\Delta L}{L \Delta T}
\]
If the uncertainty in the original length is \( \delta L \), write an expression for calculating the uncertainty in \( \alpha \).
\[
\delta \alpha/\alpha =
\]
\[
\delta \alpha =
\]
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