Physics
Temperature after a time
The gap shrinks exponentially towards the ambient temperature.
The Formula
T(t) = Ta + (T0 - Ta) x e^(-kt)
The gap shrinks exponentially towards the ambient temperature.
| Symbol | Meaning | Unit | Notes |
|---|---|---|---|
| T(t) | Temperature | degrees | The temperature after time t. |
| Ta | Ambient | degrees | The temperature of the surroundings. |
| T0 | Initial | degrees | The starting temperature of the object. |
| k | Cooling constant | per unit time | The fractional rate the gap shrinks at. |
What Each Symbol Means
T(t)degrees
Temperature
The temperature after time t.
Tadegrees
Ambient
The temperature of the surroundings.
T0degrees
Initial
The starting temperature of the object.
kper unit time
Cooling constant
The fractional rate the gap shrinks at.
See It Worked With Real Numbers
A formula on its own does not tell you which number goes where. The how to calculate newton's law of cooling page applies this equation to a concrete case, shows every intermediate step, and names the mistakes that produce a wrong answer even when the algebra is right.
Where This Formula Appears
This equation is the working core of How To Calculate Newton's Law Of Cooling, filed under Science. Every number the guide produces comes from substituting into this one line.