Thermal Law of Newton in Terminal Physics

This page introduces the loi phénoménologique de Newton (Newton's law of cooling) in the context of terminal-level physics. It outlines the scenario where the law applies and derives the governing differential equation.

The law considers a homogeneous body at temperature T in a constant temperature environment Tthermostat. The thermal power transfer causes the body's temperature to change from T(t) to T(t + Δt) over a small time interval.

Definition: The internal energy change is given by ΔU = mC(T(t + Δt) - T(t)), where m is mass and C is specific heat capacity.

An energy balance shows that the heat transfer Q equals the internal energy change ΔU (assuming no work is done). Taking the limit as Δt approaches zero leads to the differential form of Newton's cooling law.

Highlight: The key equation is mC(dT/dt) = hS(Tth - T), where h is the heat transfer coefficient and S is the surface area.

This first-order differential equation describes the rate of temperature change of the body. It forms the basis for analyzing many thermal systems and cooling processes.

Vocabulary:

• Puissance thermique: Thermal power
• Bilan d'énergie: Energy balance
• Équation différentielle: Differential equation