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MotionLab
Hot coffee, crime scene forensics, and industrial cooling — all governed by the same exponential decay.
Newton's law of cooling says the rate of temperature change is proportional to the temperature difference — this produces an exponential decay curve where the object cools quickly at first (large difference) and progressively slower as it approaches ambient temperature, never quite reaching it.
Forensic investigators use this law to estimate time of death from body temperature. Food safety guidelines use it to determine safe cooling times. HVAC engineers use it to size heating and cooling systems. The same simple equation appears across surprisingly diverse fields.
Final temperature (°C)
30.939
T(t) = T_env + (T₀ − T_env)·e^(−kt)
What you entered
Initial temperature difference
95 − 22= 73 °CT(t) = T_env + (T₀ − T_env)·e^(−kt)
22 + 73 × e^(−0.07 × 30)= 30.9393 °CResult
Final temperature (°C): 30.939
Starting at 95°C in a 22°C environment, after 30 minutes the object cools to 30.94°C.