Why Does Concrete Contract Differently in Cold Temperatures?

In summary, linear thermal expansion is the change in length of a material when its temperature changes. This is caused by the movement of molecules within the material, which increases the space between them. It can be measured using a dilatometer and is represented by the coefficient of linear expansion, which measures how much a material expands or contracts per unit length for every degree change in temperature. Linear thermal expansion has practical applications in everyday life, such as in metal bridges and train tracks, as well as in materials like thermometers, bimetallic strips, and thermostats.
  • #1
titusdna
2
0
Got this question wrong on this weeks physics quiz and can't figure out why. I keep getting the same answer - which was wrong - over and over. What am I missing?

By how much will a slab of concrete 18 m long contract when the temperature drops from 24 °C to -16 °C? (The coefficient of linear thermal expansion for concrete is 10-5 per degree C.)
Answers are in centimeters.
Formula:
change in length= a* Lo* change in temp
Lo = 1800cm
A = 10-5
change in T = 24- (-16) = 40
I keep coming up with .7 cm
the answer was .5cm
Where did I go wrong? Any help greatly appreciated
Thank you
 
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  • #2
I can't find an error in your calculations. Maybe the result was rounded in the answers or there's a typo somewhere?
 
  • #3
for reaching out for help with this question. It seems like you have the correct formula and values, so let's go through the steps to see where the error may have occurred.

First, let's check the units. The coefficient of linear thermal expansion is given in 10^-5 per degree C, so we need to make sure that our temperature change is also in degrees Celsius. In this case, 24 °C to -16 °C would be a change of -40 °C, not 40 °C.

Next, let's double check the calculation. Using the formula, we get:
change in length = (10^-5) * 1800cm * (-40 °C) = -0.72 cm
So it looks like the answer should be -0.72 cm, which is close to the answer you were getting. However, the question asks for the change in length in centimeters, so we need to take the absolute value of this answer. This gives us a final answer of 0.72 cm, which is closer to the given answer of 0.5 cm.

It's possible that there was a rounding error at some point in the calculations, or an incorrect unit conversion. Make sure to always double check your units and calculations to avoid any errors. I hope this helps and good luck on your future quizzes!
 

Related to Why Does Concrete Contract Differently in Cold Temperatures?

What is linear thermal expansion?

Linear thermal expansion refers to the change in length of a material when its temperature changes. When a material is heated, its molecules gain energy and vibrate more, causing the material to expand. This expansion is predictable and can be calculated using the material's coefficient of linear expansion.

What causes linear thermal expansion?

The movement of molecules in a material causes linear thermal expansion. As a material is heated, its molecules gain kinetic energy and vibrate more, causing the material to expand. This expansion is due to the increased space between molecules.

How is linear thermal expansion measured?

Linear thermal expansion is typically measured using a device called a dilatometer. This instrument measures the change in length of a material as it is heated or cooled. The results from a dilatometer test can be used to calculate the material's coefficient of linear expansion.

What is the coefficient of linear expansion?

The coefficient of linear expansion is a measure of how much a material expands or contracts per unit length for every degree change in temperature. It is typically represented by the symbol α and is expressed in units of 1/K (kelvin) or 1/°C (degrees Celsius).

How does linear thermal expansion impact daily life?

Linear thermal expansion is a phenomenon that can be seen in everyday objects. For example, metal bridges and train tracks have expansion joints to allow for the expansion and contraction of the metal due to temperature changes. This principle is also used in materials such as thermometers, bimetallic strips, and thermostats.

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