Two cylindrical rods are made of the same material and have the same length but one is hollow and other is solid. Both are heated to same increase in temperature. Which rod expands more?
From my understanding of linear thermal expansion, linear thermal expansion only depends on the expansion coefficient, the length of the material, and the change in temperature. Shouldn't the rods expand equally?
yes. They expand equally
As we know both rods have same value of coefficient ,temperature and length so there will be same expansion in both
Based on your understanding of linear thermal expansion, it seems logical to think that the two rods would expand equally since they are made of the same material, have the same length, and are subjected to the same increase in temperature. However, there is an additional factor that needs to be considered - the cross-sectional area of the rods.
When a solid rod is heated, it expands uniformly in all directions because there are no empty spaces inside to restrict the expansion. On the other hand, a hollow rod has an empty space inside, thereby reducing the amount of material that can expand. As a result, a hollow rod expands less than a solid rod of the same length when subjected to the same increase in temperature.
To understand this concept more intuitively, imagine two cylindrical rods made of the same material and having the same length. Now, consider that the solid rod has a certain mass distributed throughout its cross-section. When this solid rod is heated, all parts of its cross-section expand uniformly.
However, in the case of the hollow rod, the mass is concentrated around the outer circumference, leaving an empty space inside. This internal void restricts the expansion of the rod's cross-section. As a result, the solid rod will experience a greater increase in diameter compared to the hollow rod, causing it to expand more overall.
So, even though linear thermal expansion is primarily determined by the material's coefficient of thermal expansion, length, and change in temperature, the cross-sectional area also plays a crucial role in determining the magnitude of expansion. In this case, the solid rod, having more mass distributed across its entire cross-section, expands more than the hollow rod with its concentrated mass around the outer circumference.