Newton's Law of Cooling (dQ/dt = −k(T₂ − T₁) → T₂ = T₁ + C'e^{−Kt})
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dQ/dt = −k(T₂ − T₁) → T₂ = T₁ + C'e^{−Kt}
What each symbol means
| Symbol | What it stands for |
|---|---|
| K | k/(ms) where m is mass and s is specific heat |
| k | Positive constant depending on surface area and nature of surface |
| t | Time (s) |
| C' | Constant determined by initial conditions |
| T₁ | Temperature of the surroundings (K or °C) |
| T₂ | Temperature of the body (K or °C) |
| dQ/dt | Rate of heat loss (W) |
When to use this
Valid only for SMALL temperature differences between body and surroundings. Rate of cooling is proportional to temperature excess. Combines conduction, convection, and radiation losses. Exponential decay: ln(T₂−T₁) vs t is a straight line with negative slope.