A hot liquid is kept in a big room. The logarithm of the numerical value of the temperature difference between the liquid and the room is plotted against time. The plot will be very nearly

As per Newton's law of cooling,

$\theta -{\theta }_0=\left({\theta }_i-{\theta }_0\right)\left(e^{-kt}\right)$, where $\theta , {\theta }_0, {\theta }_i$ represent instantaneous temperature of the body, temperature of the surrounding, initial temperature of the body respectively.

The graph of $\theta$ versus $t$ is exponentially decaying graph (resembling hyperbolic graph)

$\ln \left(\theta -{\theta }_0\right)=\ln \left({\theta }_i-{\theta }_0\right)-kt$

The graph of $\ln \left(\theta -{\theta }_0\right) \mathrm{versus} t$ is a straight line with positive intercept and negative slope.