Thermal expansion, percent change in density problem

In summary, thermal expansion is the tendency of matter to change in volume in response to a change in temperature. It is measured using the coefficient of thermal expansion (CTE) and can be calculated using a specific formula. In everyday life, thermal expansion can be seen in the expansion and contraction of various objects, such as bridges and glass bottles. In engineering and construction, CTE values are used to design structures that can withstand thermal expansion and prevent damage.
  • #1
ctpengage
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Homework Statement



When the temperature of a metal cylinder is raised from 0.0°C to 100°C, its length increases by 0.23%. Find the percent change in density.


Homework Equations


∆L = L∆T
p=m/v

The Attempt at a Solution



I don't have any real idea how to start the problem. How do I relate the change in length to the change in volume? I know that mass is constant.

Thanks
 
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  • #2
How do you find the volume of a cylinder? Hint: All linear dimensions increase by the same percentage.
 
  • #3
oh my god thanks so much
 

What is thermal expansion?

Thermal expansion is the tendency of matter to change in volume in response to a change in temperature. When a material is heated, its particles vibrate faster and take up more space, causing the material to expand.

How is thermal expansion measured?

Thermal expansion is measured using the coefficient of thermal expansion (CTE), which is a ratio of the change in length or volume of a material to the original length or volume at a specific temperature. It is usually expressed in units of parts per million per degree Celsius (ppm/°C) or parts per million per degree Kelvin (ppm/K).

What is the formula for calculating percent change in density due to thermal expansion?

The formula for calculating percent change in density due to thermal expansion is: [(final density - initial density) / initial density] x 100%. This calculates the percentage change in density based on the change in volume of a material due to thermal expansion.

What are some common examples of thermal expansion in everyday life?

Some common examples of thermal expansion in everyday life include the expansion and contraction of bridges, roads, and railway tracks due to temperature changes, the breaking of glass bottles when hot liquid is poured into them, and the popping of popcorn kernels when heated.

How is thermal expansion accounted for in engineering and construction?

Thermal expansion is an important factor to consider in engineering and construction, especially in structures made of materials such as concrete, steel, and glass. Engineers and architects use CTE values to determine how much a material will expand or contract with temperature changes and design structures accordingly to prevent damage or failure.

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