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A brass rod is 185 cm long and 1.60 cm in diameter. What force must be applied to each end of the rod to prevent it from contracting when it is cooled from 120.0°C to 10.0°C?
20. Heat and Temperature
Volume Thermal Expansion
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If a block of aluminum has a volume of exactly at , what is its volume at ? The coefficient of linear expansion for aluminum is.
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Verified step by step guidance1
Understand that the problem involves thermal expansion, which is the tendency of matter to change in volume in response to a change in temperature.
The volume expansion can be calculated using the formula: V = V0 * (1 + β * ΔT), where V0 is the initial volume, β is the coefficient of volume expansion, and ΔT is the change in temperature.
Since the problem provides the coefficient of linear expansion (α), we need to convert it to the coefficient of volume expansion (β). For isotropic materials like aluminum, β = 3 * α.
Calculate the change in temperature (ΔT) by subtracting the final temperature (0°C) from the initial temperature (1000°C).
Substitute the values into the volume expansion formula: V = 1.00 cm³ * (1 + 3 * 2.30×10⁻⁵ °C⁻¹ * (0°C - 1000°C)) to find the final volume at 0°C.
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