Key Concepts

• • T(t) = T_env + (T₀ − T_env) · e^(−kt)
• • Rate of cooling ∝ temperature difference: dT/dt = −k(T − T_env)
• • Time constant τ = 1/k: at t = τ, excess above ambient falls to 1/e ≈ 36.8%
• • After 5τ the object is practically at ambient temperature (<1% excess)
• • Applications: forensics (time of death), food safety, heat exchanger design
• • k depends on surface area, convection coefficient, and thermal capacity