Thermal Expansion: How to Loosen a Jar Lid

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. 在热膨胀过程中，每个线性尺寸随着温度的升高都会增加相同的百分比，包括孔洞。这假设膨胀材料是均匀的。将此原理应用于金属罐盖时，这意味着罐盖的内径会增加，从而倾向于松开罐盖。将热水流直接对着罐盖中心加热，会使金属部分比玻璃部分加热得更多，因此罐盖顶部和罐体之间的膨胀差异会更大。金属盖的热导率远高于玻璃，其比热容相对较低，因此整个金属盖的温度会迅速上升。 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. 即使你对金属盖和玻璃罐均匀加热，盖子也会稍微松开，因为金属的热膨胀系数大于玻璃的。

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.

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

Fortunately, even this small amount of expansion is sometimes sufficient to enable you to remove a stubborn lid.

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. 在松开罐盖的例子中，实验表明，通过加热可以松开玻璃罐的钢制盖子，因为钢的热膨胀系数大于玻璃。但这是有点微妙的，因为钢的膨胀只是玻璃的1.44倍，而且两者的膨胀都很小。将热水流直接对着盖子中心加热，会使金属部分比玻璃加热得更多，从而产生顶部和罐体之间更大的膨胀差异。这可以实现的原因是钢盖的热导率几乎是玻璃的63倍。

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.