A hot liquid is kept in a big room. Its temperature is plotted as a function of time. Which of the following curves may represent the plot?

 

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.