Question

The temperature of a 1 m long aluminum rod is 20° C. If the temperature is increased to 70° C, what is the
length of the rod?

Answer 1

Answer on Question 49189, Physics, Mechanics | Kinematics | Dynamics

Question:

The temperature of a 1 m long aluminum rod is 20°C. If the temperature is increased to 70°C, what is the length of the rod?

Solution:

By the definition of the linear thermal expansion we have:

$$\Delta L _ {a} = \alpha_ {a} L _ {0 a} \Delta T,$$

where $\Delta L_{a}$ is the change in the length of the aluminum rod after the change of temperature, $\alpha_{a} = 23\cdot 10^{-6}\mathrm{{}^\circ C^{-1}}$ is the coefficient of linear expansion for aluminum, $L_{0a}$ is the length of the aluminum rod before the change of temperature, $\Delta T$ is the change of temperature.

Therefore, substituting all data from condition of the problem to the formula for linear thermal expansion we obtain:

$$\Delta L _ {a} = 23 \cdot 10^{-6} \mathrm{{}^\circ C^{-1}} \cdot 1 \mathrm{m} \cdot (70{}^{\circ} \mathrm{C} - 20{}^{\circ} \mathrm{C}) = 0.00115 \mathrm{m}.$$

Then the length of the aluminum rod would be:

$$L = L _ {0 a} + \Delta L _ {a} = 1 \mathrm{m} + 0.00115 \mathrm{m} = 1.00115 \mathrm{m}.$$

Answer:

The length of the aluminum rod is 1.00115 meters.

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