notes

Cooling

sd cooling coffee

Example: Cooling a hot cup of coffee. Stock: Coffee temperature $T$. Flow: Heat loss to the environment $kT$. Behavior: Temperature decreases towards room temperature $T_{\rm room}$. Equation: $$\tag{SD3} \frac{dT}{dt} = -k(T - T_{\rm room}), $$        where $k$ is the cooling rate. Diagram: graph LR; Coffee -->|Loses Heat| Environment Environment -->|Gains Heat| Coffee