Volumetric Expansion and Overflow

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In summary, the beaker of volume V = 1.90 L, filled with turpentine at T1 = 11.0 °C, will overflow by 3.41e-05 m3 when the temperature reaches T2 = 30.0 °C due to the volumetric expansion coefficient of turpentine. The calculation using deltaV = β x deltaT x V results in a similar but slightly different value, which may be due to other factors not considered in the calculation. Further analysis may be needed to determine the exact reason for the discrepancy.
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mexqwerty
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A glass beaker of volume V = 1.90 L is filled with turpentine when the temperature is T1 = 11.0 °C. The linear expansion coefficient for glass is αglass = 9.13 × 10–6 K–1 and the volumetric expansion coefficient for turpentine is βturpentine = 9.72 × 10–4 K–1. How much turpentine will overflow the beaker when the temperature will reach T2 = 30.0 °C?

The answer is 3.41e-05 m3.

I used deltaV = β x deltaT x V
deltaV = 9.72e-4 x (30-11) x (1.9e-3) = 3.51e-05 m3. It's not the same as the answer but its close. Is that just a coincidence? What have I done wrong?
 
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To determine the overflow of turpentine you have to consider the volume expansion of the beaker along with that of turpentine.
 

FAQ: Volumetric Expansion and Overflow

What is volumetric expansion?

Volumetric expansion, also known as thermal expansion, is the increase in volume of a substance when its temperature increases. This is due to the individual particles of the substance moving faster and taking up more space.

How is volumetric expansion measured?

Volumetric expansion is typically measured in terms of the coefficient of thermal expansion (CTE), which is the change in volume per unit change in temperature. It is expressed in units of length per unit length per degree Celsius (or Kelvin).

What are some examples of materials with high volumetric expansion?

Liquids, gases, and most solids have a higher volumetric expansion compared to other materials. Some examples of materials with high volumetric expansion include water, mercury, and aluminum.

What is the purpose of considering volumetric expansion in engineering and construction?

Volumetric expansion must be taken into account in engineering and construction to prevent damage to structures due to changes in temperature. If a material is unable to expand, it may cause stress and potential failure in the structure.

What is overflow and how does it relate to volumetric expansion?

Overflow occurs when a substance cannot expand any further and begins to spill or overflow from its container. This can happen when a substance is heated and its volume increases beyond the capacity of the container. Volumetric expansion is directly related to overflow as it is the cause of the overflow phenomenon.

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