JEE Main · 2013 · 07 Apr 2013 · Offline · Heat & Thermodynamics

Newton's law of cooling makes the rate of fall proportional to how far the body sits above the room, $\frac{dT}{dt}\propto -(T-{\theta }_0)$, whose solution is the exponential approach $T={\theta }_0+(\theta -{\theta }_0)e^{-kt}$. The temperature slides down steeply at first, while the gap is large, then eases off and flattens towards ${\theta }_0$ without ever crossing it. The matching graph is the concave exponential decay settling onto the room temperature.