= Thermal time constant
{title2=$\tau=C/G$}
A <thermal time constant> characterizes exponential relaxation in a first-order <lumped thermal model>. For <heat capacity> $C$ and <thermal conductance> $G$ to a fixed bath, a small temperature deviation obeys $C\dot{\delta T}=-G\delta T$, giving
$$
\delta T(t)=\delta T(0)e^{-t/\tau},\qquad \tau=C/G.
$$
After one $\tau$, the initial deviation has fallen to $1/e$ of its original value. The ratio has units of <time> because $C$ is measured in $\mathrm{J\,K^{-1}}$ and $G$ in $\mathrm{W\,K^{-1}}$.
A heating step provides an experimental check: the body approaches its final temperature rise with the same $\tau$ in this linear model. Greater <heat capacity> slows changes, while greater <thermal conductance> speeds exchange. Several coupled regions generally produce several relaxation modes, so fitting one exponential over a short interval does not establish a unique time constant for the entire apparatus.
Back to article page
