Thermal equilibrium

When two bodies at different temperatures are brought into contact, thermal energy flows from the hotter to the colder one until a common temperature is reached. This too is a conservation-of-energy problem: nothing new compared with mechanical balances, except that here the reservoir in play is the thermal energy of each body.

The idea is that, in an isolated system, the thermal energy given up by the hot body equals exactly that gained by the cold body. The hot body cools, the cold body heats up, and the process continues until both reach the same final temperature: from that moment on there’s no imbalance left to drive energy to flow one way or the other. The common equilibrium temperature is the intermediate value for which the books balance, that is, for which the loss of one matches the gain of the other.

Since the thermal energy of each body is $E_\text{term} = m\,c_s\,T_K$, the balance depends on three ingredients for each body: its mass, its specific heat and its temperature. A body with a large mass or a large specific heat “weighs” more in the balance, and pulls the equilibrium temperature towards its own initial value: this is why a large mass of lukewarm water is barely heated at all by a small red-hot object immersed in it.

Warning

In the thermal-equilibrium equation, temperatures must always be in kelvin ($T_K = T_{°C} + 273$). Thermal energy is $E_{\text{term}} = m\,c_s\,T_K$.

This warning isn’t a formal quibble: using degrees Celsius instead of kelvin alters the values of $E_\text{term}$ and skews the balance, especially when negative Celsius temperatures appear, which remain positive in kelvin. Converting all temperatures to kelvin before writing the calorimetric equation is the step that guards against the most insidious errors.

Links

Topics: Lavoro ed energia Concepts: Energia termica da attrito · Calore specifico e capacità termica · Conservazione dell’energia meccanica Skills: Equazione calorimetrica Objects: Calorimetro

Related exercises: Problema — Acqua e olio a temperature diverse · Problema — Roccia vulcanica nella Fanta · Esercizio svolto — blocco su piano inclinato con molla e attrito