Question

One rod is made of lead and another from quartz. The rods are heated and experience the same change in temperature. The change in length of each rod is the same:

a) True, because both materials have similar coefficients of thermal expansion
b) False, because the change in length depends on the specific heat capacity of the material
c) True, because the change in length is always independent of the material
d) False, because lead and quartz have different melting points

Answer 1

The change in length of two rods, one lead and one quartz, heated with the same temperature change will be different, as it depends on the thermal expansion coefficient of the materials, not their melting points or specific heat capacity.

Step-by-step explanation:

The answer to the student's question is False, because the change in length depends on the material's thermal expansion coefficient, not on the melting point or specific heat capacity. Each material, whether it is lead or quartz, has a unique coefficient of thermal expansion that determines how much it will expand or contract when the temperature changes. Assuming both rods experience the same change in temperature, the rod made of the material with the higher coefficient of thermal expansion will change in length more.

As an example, if we have a rod made of a certain material with a thermal expansion coefficient α, and the temperature is raised from 300 K to 600 K, the new length after heating would be (1 + 300α)(1 m). If the rod is then cooled back down to 300 K, the length will be (1 - 300α)(1 + 300α)(1 m). In theory, the length should return to 1 meter, but in practice, the relation ΔL = αLΔT is only strictly true for small temperature changes (ΔT), due to the non-linearity for larger temperature ranges. When thermal expansion coefficients are small, the discrepancy is minor and usually negligible.