b) Raktima was given some beads and a glass jar with a lid. How can she use these to explain why solid
has a definite volume and a definite shape?
Answers
Answer:
During thermal expansion, every linear dimension increases by the same percentage with an increase in temperature, including holes. This assumes that the expanding material is uniform. Applied to a metal jar lid, this implies that the inside diameter of the lid will increase, tending to loosen the lid. Directing the stream of hot water at the center of the lid heats the metal more than the glass, so that you get a greater difference in the expansion of the top and the jar. The thermal conductivity of the metal top is much greater than that of the glass, and its specific heat is relatively low, so the temperature of the entire metal lid rises rapidly.
Even if you heated the metal lid and the glass jar equally, you would loosen the lid a bit because the thermal expansion coefficient of the metal is greater than that of the glass.
If you examine the table of thermal expansion coefficients, you will find that the expansion of a steel top is only about 40% greater than that of the glass, so it is helpful if you can heat the metal more than the glass. The fact that the thermal conductivity of the steel is over 60 times that of glass aids you in raising its temperature more than that of the glass.
!? If the thermal conductivity of steel is 60 times that of glass, why isn't the expansion coefficient 60 times as large, instead of just 1.4 x that of glass?
The amount of actual expansion is quite small since the coefficients of expansion are very small. If the 7 cm diameter lid were heated from 20°C to 60°C, the amount of expansion is only
ΔL = (7 cm)(13 x 10-6)(40°C) = 0.0036 cm
Fortunately, even this small amount of expansion is sometimes sufficient to enable you to remove a stubborn lid.
Table of expansion coefficients
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Expansion concepts
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Thermal Expansion vs Thermal Conductivity
Why do they behave so differently?
In the example of loosening a jar lid, experiment shows that you can loosen a steel lid on a glass jar by heating because the thermal expansion coefficient of steel is greater than that of glass. But it is a bit tricky, because the expansion of the steel is only 1.44 times that of the glass, and both expansions are quite small. Directing the stream of hot water at the center of the lid heats the metal more than the glass, so that you get a greater difference in the expansion of the top and the jar. This can be done because the thermal conductivity of the steel top is almost 63 times the thermal conductivity of glass.
Solid substances expand with increasing temperature because the average spacing between the nuclei increases slightly as a result of the greater kinetic energy of the molecules - they vibrate with greater amplitude and on the average find themselves a bit further apart. This kinetic energy involves the atoms as a whole and there is not such a great difference between what happens in glass and steel.
However, in thermal conductivity a new mechanism arises. In the metal there are essentially free electrons which can move through the steel. While they have no role in determining thermal expansion, they do provide a means for rapid heat transfer through the material. The same kind of argument applies to the electrical conductivity of the materials. The steel is an electrical conductor because of the mobility of the electrons through the material. The electrical and thermal conductivities can in fact be shown to be proportional to each other; this is the subject of the Wiedemann-Franz law.
Good thermal conductor <--> Good electrical conductor.
Table of expansion coefficients
Table of thermal conductivities
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Expansion concepts
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