How long should I wait to steep my tea?

$$T(t) = T_{env} + (T(0) -T_{env})e^{-t/tau}tag{1}$$

To find $tau$ we need to 'unpack' Newton's Law of Cooling a little. The law states:

$$dot{Q}=hA[T(t)-T_{env}]$$

(check your link for the meaning of the symbols)

We also know that:

$$dot{Q}=-mc_pfrac{text{d}T(t)}{text{d}t}$$

Combined we get:

$$frac{text{d}T(t)}{text{d}t}=-frac{hA}{mc_p}[T(t)-T_{env}]$$

Often we then state that:

$$frac{1}{tau}=frac{hA}{mc_p}$$

Integration then yields $(1)$.

$A$, $m$ and $c_p$ are easy to determine but $h$ is harder. Usually tabulated values of $h$ for different situations can give a crude estimate.

$tau$ can also be determined experimentally from relatively simple home experiments.

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An easier and more accurate way of controlling temperature may be by mixing water of two known temperatures in the correct ratio.

For example, say we have a mass $m_H$ of boiling hot water (at $T_H$). To it we now add a mass $m_C$ of cold water (for example iced water at $T_C$).

Assuming the mixing was adiabatic, the final temperature $T_F$ is then approximately given by:

$$m_HT_H+m_CT_Capprox (m_H+m_C)T_F$$

This formula can be used to determine $m_C$ as a function of all other variables $T_F$, $m_H$, $m_C$ and $T_C$.

You could introduce an additional constraint, like:

$$m_H+m_C=M$$

where $M$ would be the full content of a vessel, like a mug or a teapot.