Problem with Thermal expansion: volume

AI Thread Summary
To determine the percentage change in density of lead when its temperature increases from 0°C to 100°C, the thermal expansion coefficient (α) must be used correctly. The equation ΔV = Vi βΔT is relevant, but it’s important to clarify that β refers to the volumetric thermal expansion coefficient, which can be derived from the linear coefficient (α) by multiplying by three. The density of lead at 0°C is 11,300 kg/m3, and the correct approach involves accounting for three-dimensional expansion. Misapplication of the coefficients can lead to incorrect results, highlighting the need for careful consideration of thermal properties in calculations.
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Homework Statement


The temperature of a block of lead is raised from 0°C to 100°C. What is the percentage change in its density? (The density of lead at 0°C is 11,300 kg/m3.)


Homework Equations


ΔV = Vi βΔT


The Attempt at a Solution


it gave the wrong answer when i tried to use the above equation
 
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What did you use for β?

Is that a given in the problem?

I'm used to seeing β used for compressibility.

If you are using α the thermal expansion coefficient, you may need to account for expansion in 3-D, which corrects the linear α to volume α with the factor 3.

αv ≅ 3*αL

http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/thexp2.html#c3
 

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