Shaskolskaya & Eltsin Problem 195
Physics · thermodynamics · heat transfer
Problem
the ball passes through the ring at any temperature which is the same for both ball and ring. Heating the ring is equivalent to cooling the ball and consequently the ball will pass freely through the ring when the latter is heated. 196 It is important for a calorimeter that the temperature inside it should even out quickly. This is helped by metal's high thermal conductivity. Therefore the temperature evens out more quickly in a metal container than in a glass one. Besides, the specific thermal capacity of metal is less than that of glass, and this allows the water equivalent of the calorimeter to be reduced and the degree of accuracy of measurements to be increased. It is also important for a calorimeter that as little heat as possible should escape outside. In this respect too metal calorimeters have an advantage over those made of glass, since metal radiates heat less than glass.Intuitive explanation
Thermal expansion and contraction change the actual dimensions of materials—when you heat the ring, it expands uniformly in all directions, making the hole larger, while the ball either stays the same size or shrinks if cooled. The key insight is that the gap between ball and ring depends on the difference in their thermal expansion, not just their initial sizes. By understanding how linear expansion scales with temperature, you can find the condition where they fit together perfectly.
Intuitive explanation
Thermal expansion and contraction change the actual dimensions of materials—when you heat the ring, it expands uniformly in all directions, making the hole larger, while the ball either stays the same size or shrinks if cooled. The key insight is that the gap between ball and ring depends on the difference in their thermal expansion, not just their initial sizes. By understanding how linear expansion scales with temperature, you can find the condition where they fit together perfectly.