Problem — The hot water bottle

Problem

Explain, in five lines, why a rubber hot water bottle filled with hot water at $60 \ ^{\circ}\text{C}$ heats for longer than the same mass of hot sand at $60 \ ^{\circ}\text{C}$. Also explain why molten lead, at the same mass and temperature, would cause burns.

Solution

Water has a very high specific heat, about $4186 \ \text{J/(kg·K)}$, compared with about $800 \ \text{J/(kg·K)}$ for sand. For the same mass and temperature, water therefore stores about five times more thermal energy: as it cools it releases more heat, and for a longer time. Lead, at $60 \ ^{\circ}\text{C}$, is solid and shows no special behaviour, but if it is brought above $327 \ ^{\circ}\text{C}$ it becomes liquid. On resolidifying it would release the latent heat of solidification in addition to its specific heat, giving off an enormous amount of energy at a much higher temperature, causing serious burns. What matters is the stored energy, given by $m \, c \, \Delta T$ plus any latent heat, not temperature alone (Bloomfield 2016) Riferimenti bibliografici.

Collegamenti

Argomenti: Termologia Concetti: Calore specifico e capacità termica · Calore latente e cambiamenti di stato