How this calculator works
When heat loss is proportional to the temperature difference from a fixed environment, a lumped energy balance produces exponential decay of that difference. The rate constant has units 1/s and equals hA/C for constant convection coefficient and total heat capacity. The model also describes warming toward a warmer ambient. Large internal gradients, changing ambient conditions or strong radiative effects require a different model.
Formula
T(t) = Ta + (Ti - Ta) exp(-kt); k = hA/C; t = -ln[(T - Ta)/(Ti - Ta)]/k.
Worked example
A body starting at 353.15 K in 293.15 K air with k = 0.01/s reaches 323.15 K after 69.3147181 s. After twice that time, it reaches 308.15 K.
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Frequently asked questions
Can the body cross ambient temperature?
Not under this model with positive rate and fixed ambient temperature. It approaches ambient asymptotically.
When is a uniform body temperature reasonable?
A Biot number below about 0.1 is a common first check, together with the accuracy needed.
Is the rate constant a time?
No. It is inverse time; its reciprocal is the thermal time constant.