Thermal energy and specific heat

When friction takes energy away from motion, that energy doesn’t vanish: it settles into the bodies as thermal energy, the energy associated with the microscopic agitation of particles. We can quantify it exactly, both from the side of the cause (the work dissipated by friction) and from the side of the effect (the temperature rise of the body storing it).

Key formula

$\Delta E_{\text{term}} = |\vv{F}_a|\cdot|\Delta\vv{s}|$ $E_{\text{term}} = m\,c_s\,T$ where $c_s$ = specific heat

The first relation links the increase in thermal energy to the work of friction: every joule taken from the motion by sliding a distance $|\Delta\vv{s}|$ against a force $|\vv{F}_a|$ reappears as heat. The second relation instead describes where that heat ends up: the thermal energy stored in a body grows with its mass $m$, with its temperature $T$, and with a constant characteristic of the material, the specific heat $c_s$.

Specific heat measures how much energy is needed to heat one kilogram of a substance by one degree: materials with a high $c_s$ (such as water) are “roomy” — they absorb a lot of energy while heating up only a little; materials with a low $c_s$ heat up quickly for the same energy received. This is why, combining the two formulas, we can predict exactly how much a braking block actually heats up: the energy $|\vv{F}_a|\cdot|\Delta\vv{s}|$ dissipated by friction spreads through the body according to its $m\,c_s$, and produces a temperature rise that is smaller the more massive or thermally roomy the body is.

In the energy table this translates into a concrete move: a column is added for $E_{\text{term}}$. While the kinetic- and potential-energy columns can rise and fall along the motion, exchanging values, the $E_{\text{term}}$ column can only grow. Its increase between one state and the next is exactly the work of friction done in that stretch, and keeping track of it in a dedicated column guarantees that the total energy balance stays closed even in the presence of dissipation.

Links

Topics: Lavoro ed energia Concepts: Energia termica da attrito · Calore specifico e capacità termica · Attrito dinamico Skills: Uso della tabella energetica Methods: Tabella energetica a stati

Related exercises: Problema — Blocco spinto con attrito · Esercizio svolto — blocco su piano inclinato con molla e attrito · Problema — Spingere una cassa in moto