Core answer: Q=cmΔT — water at 4186 J/(kg·℃) tops common substances, so 1L from 20℃ to boiling takes 336kJ; wind chill converts wind speed into felt temperature (-5℃ with 40km/h wind feels ≈ -12℃); decibels are logarithmic — +10dB means 10× energy and about 2× perceived loudness, with 85dB the 8-hour exposure limit.
Specific heat and boiling cost
Q=cmΔT: heat = specific heat × mass × temperature rise. Boiling 1L water (ΔT=80℃): Q=4186×1×80=335kJ — at $0.08/kWh roughly 1 cent; a 2000W induction stove needs ~168s theoretically, 3-4 min with pot losses.
Specific heat table
| Substance | J/(kg·℃) | Meaning |
|---|---|---|
| Water | 4186 | natural heat reservoir |
| Ethanol | 2440 | heats easier than water |
| Sand/stone | ~800 | 1/5 of water — desert swings |
| Iron | 450 | pans heat fast |
| Copper | 385 | quick to heat, poor storage |
| Air | 1005 | what heaters mainly warm |
Wind chill table
Wind chill (Canada 2001 formula) expresses wind-driven heat loss as an equivalent still-air temperature:
| Air temp | 20km/h | 40km/h | 60km/h |
|---|---|---|---|
| 0℃ | -5℃ | -8℃ | -10℃ |
| -5℃ | -11℃ | -12℃ | -15℃ |
| -10℃ | -16℃ | -18℃ | -21℃ |
Below -28℃ equivalent, exposed skin can frostbite in 10-30 minutes.
Reading the dB scale
dB=10lg(P/P₀): +3dB doubles energy; +10dB roughly doubles loudness.
| Scene | dB | Risk |
|---|---|---|
| Whisper | 30 | safe |
| Conversation | 60 | safe |
| Hair dryer | 70-80 | caution long-term |
| Subway car | 80-90 | 85dB/8h ceiling |
| Concert front row | 110-120 | damage in minutes |
| Jet engine | 130+ | instant pain |
100dB is not “twice 50dB” — it is 100,000× the energy.
Example: mild coastal climate
Under identical sunshine, sand (~800) heats 5× easier than water (4186). The sea soaks daytime heat with barely a degree of rise and releases it at night — trimming coastal day-night swings by 5-10℃ versus inland. That is the maritime climate in one number.
Example: hair dryer vs concert
A dryer at 80dB for 10 minutes daily sits far below the 85dB/8h ceiling — safe. A concert at 110dB: applying “halve safe time per +3dB”, +25dB halves the 8h limit about 8 times → ~2 minutes. Two hours unprotected means irreversible hair-cell damage.
Common pitfalls
- “dB adds linearly”: two 80dB sources give 83dB, not 160 — doubled energy is just +3dB.
- “Wind chill freezes pipes above 0℃”: wind only speeds cooling; nothing drops below actual air temperature.
- “High specific heat heats fast”: opposite — water resists both heating and cooling, hence copper hotpots (fast) and water-based warmers (slow).
- “0dB is silence”: 0dB is the hearing-threshold reference, not no-sound; negative dB exists physically.