Thermodynamics (Heat expansivity)

In summary, to prevent the tiles from buckling, a minimum gap of 2.76 meters must be left between them when they are laid.
  • #1
Aleisha
25
0

Homework Statement


A concrete driveway is built from identical slabs of concrete, as shown below, which have a length, L, of 3.18 m long at 17.3 C. The concrete slabs have coefficient of linear expansion of 1.20 x 10-5 K-1 and are laid in an area where the temperature ranges from -29.8 C to 42.6 C.
Calculate the minimum lengthwise gap (Δx) that should be left between the tiles when they are laid to ensure that the tiles do not buckle when the temperature changes.

Homework Equations


Change in length=coefficient of linear expansion x original length x change in temp (Kelvin)

The Attempt at a Solution


Change in length (x)= (1.20e-5) x 3.18 x 72.4
=2.76e-3m
Answer was wrong but am confused as to how else to do it with any other equation i think i may have made an error with conversions or values needing to be used?
 
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  • #2
Aleisha said:

Homework Statement


A concrete driveway is built from identical slabs of concrete, as shown below, which have a length, L, of 3.18 m long at 17.3 C. The concrete slabs have coefficient of linear expansion of 1.20 x 10-5 K-1 and are laid in an area where the temperature ranges from -29.8 C to 42.6 C.
Calculate the minimum lengthwise gap (Δx) that should be left between the tiles when they are laid to ensure that the tiles do not buckle when the temperature changes.

Homework Equations


Change in length=coefficient of linear expansion x original length x change in temp (Kelvin)

The Attempt at a Solution


Change in length (x)= (1.20e-5) x 3.18 x 72.4
=2.76e-3m
Answer was wrong but am confused as to how else to do it with any other equation i think i may have made an error with conversions or values needing to be used?
The slabs are laid at 17.3 degrees. If the temperature goes down to -29.8 C, the slabs get shorter so they can't buckle. They can only get longer at temperatures above 17.3 C.
 
  • #3
So technically to get the correct answer i have to minus 17.3 from the highest temp i.e. 42.6-17.3=25.3 C? And that will be my change in temp and everything else stays the same?
 
  • #4
Aleisha said:
So technically to get the correct answer i have to minus 17.3 from the highest temp i.e. 42.6-17.3=25.3 C? And that will be my change in temp and everything else stays the same?
Yes. But, you need to take into account that both slabs grow by this amount. On the other hand, they didn't tell you where the slabs are anchored. I guess you need to assume that they are anchored at their opposite ends.
 
  • #5
Thank you!
 

Related to Thermodynamics (Heat expansivity)

1. What is thermodynamics and why is it important?

Thermodynamics is the branch of physics that deals with the relationship between heat and other forms of energy. It is important because it helps us understand how energy is converted from one form to another, and how it affects the behavior of matter.

2. What is heat expansivity?

Heat expansivity, also known as thermal expansivity, is the property of a material to expand when heated and contract when cooled. It is a measure of how much a substance's volume changes with a change in temperature.

3. How does heat expansivity affect different materials?

Heat expansivity affects different materials in different ways. Materials with high expansivity, such as metals, will expand and contract significantly with changes in temperature. On the other hand, materials with low expansivity, like glass, will expand and contract very little.

4. What is the coefficient of thermal expansion?

The coefficient of thermal expansion is a measure of the rate at which a material expands or contracts with a change in temperature. It is typically expressed in units of length per unit length per degree Celsius (or Kelvin).

5. How is thermodynamics and heat expansivity used in real life?

Thermodynamics and heat expansivity have many practical applications in everyday life. For example, they are used in the design of bridges and buildings to account for the expansion and contraction of materials due to changes in temperature. They are also used in the development of heating and cooling systems, as well as in the production of various materials and products.

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