homework and exercises - What does 1/k represent regarding Newtons Law of Cooling?

What does 1/k represent regarding Newtons Law of Cooling?
I know k represents the cooling constant. I think the inverse of k is the time taken for the liquid to cool from its maximum temperture to surrounding temperature. Any clarification would be most appreciated.

Answer

In Newton's law of cooling, the constant $k$ appears in most solutions schematically as,$^\dagger$

$$T(t)\sim e^{-kt}$$

Clearly, the argument of the exponential must be dimensionless, hence the constant $k$ has dimensions,

$$[k]=\frac{1}{[\mathrm{time}]}$$

The constant $k$ is a measure of the rate of cooling, with the same dimensions as a frequency.

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$\dagger$ We have assumed the simplest formulation of Newton's law of cooling, wherein the system of differential equations are linear, with constant coefficients.