Simple Newton's Law assumes heat only flows to the air. But when you pour boiling water into a cold ceramic cup, two things happen:
The cold cup absorbs heat from the water. A 252g ceramic cup at 20°C can absorb enough heat to drop water temperature by 10-15°C. This happens quickly (τ ≈ 3-5 min).
Heat escapes to the surrounding air via convection and radiation. This is slower (τ ≈ 40-50 min) because air is a poor heat conductor.
The two-exponential model captures both:
T(t) = T_amb + A₁·e^(-k₁t) + A₂·e^(-k₂t)
This reduces RMSE from ~2.4°C (simple Newton) to ~0.5°C, especially improving accuracy in the critical first 10 minutes.
If you pre-heat the cup with hot water first, A₁ → 0 and you get simple Newton cooling.
Tea contains several methylxanthine alkaloids—psychoactive compounds that affect the nervous system.
The primary stimulant. Blocks adenosine receptors, promoting alertness. Half-life: 3-7 hours.
Bronchodilator and mild stimulant. Used medically for asthma.
Milder stimulant than caffeine. Longer half-life (~7 hours). Also found in chocolate.
| Tea Type | Caffeine | L-Theanine |
|---|---|---|
| Black | 40-70mg | 24mg |
| Oolong | 30-50mg | ~20mg |
| Green | 20-45mg | ~20mg |
| White | 15-30mg | ~18mg |
| Herbal/Rooibos | 0mg | 0mg |
Values per 240ml cup.
Caffeine content varies even among teas from the same plant (Camellia sinensis) due to processing and leaf selection. Young buds and tips contain more caffeine than mature leaves. Oxidation during processing (full for black, partial for oolong, minimal for green/white) also affects extraction rates—more oxidized leaves release caffeine faster when brewed. Steeping time and water temperature matter too: hotter water and longer steeps pull out more caffeine.
Not a xanthine, but notable: this amino acid unique to tea promotes calm alertness by increasing alpha brain waves, modulating caffeine's effects.
Black tea: Add at 95°C, steep 3-5 min.
Green tea: Add at 75-80°C, steep 2-3 min.
White tea: Add at 75°C, steep 3-5 min.
Oolong: Add at 85-90°C, steep 2-4 min.
Herbal infusions: Add at 100°C, steep 5-7 min.
Rooibos: Add at 100°C, steep 5-7 min. Won't turn bitter.
Above 65°C: Risk of oral burns. WHO classifies beverages above 65°C as "probably carcinogenic" with repeated exposure.
60-65°C: Hot but generally safe. Flavor compounds are volatile.
55-60°C: Comfortable drinking zone for most people.
45-55°C: Lukewarm. Flavor becomes less vibrant.
Below 45°C: Cold tea. Different flavor profile.
The chart shows a blue "ideal" zone between your drinkable temperature and the "too cold" threshold, and a gray "cold" zone below that.
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