Questions: The temperature of a 2 m aluminum rod is increased by (400^circ mathrmC). What is the new length of the aluminum rod? (mathrma=23 times 10^-6 / ^circ mathrmC)

Solution Steps

We are given:

• Initial length of the aluminum rod, \( L_0 = 2 \) m
• Temperature increase, \( \Delta T = 400^{\circ} \mathrm{C} \)
• Coefficient of linear expansion for aluminum, \( \alpha = 23 \times 10^{-6} /^{\circ} \mathrm{C} \)

The formula for linear expansion is: \[ \Delta L = \alpha L_0 \Delta T \] where:

• \( \Delta L \) is the change in length
• \( \alpha \) is the coefficient of linear expansion
• \( L_0 \) is the initial length
• \( \Delta T \) is the change in temperature

Substitute the given values into the formula: \[ \Delta L = (23 \times 10^{-6} /^{\circ} \mathrm{C}) \times 2 \, \mathrm{m} \times 400^{\circ} \mathrm{C} \] \[ \Delta L = 23 \times 10^{-6} \times 2 \times 400 \] \[ \Delta L = 0.0184 \, \mathrm{m} \]

The new length \( L \) is the initial length plus the change in length: \[ L = L_0 + \Delta L \] \[ L = 2 \, \mathrm{m} + 0.0184 \, \mathrm{m} \] \[ L = 2.0184 \, \mathrm{m} \]

Final Answer