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(B) According to Newton's law of cooling,the rate of loss of heat $(dQ/dt)$ of a body is directly proportional to the difference in temperature betwee

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(B) According to Newton's law of cooling,the rate of loss of heat $(dQ/dt)$ of a body is directly proportional to the difference in temperature between the body and its surroundings,provided the temperature difference is small. Mathematically,$-dT/dt = k(T - T_0)$,where $T$ is the temperature of the body,$T_0$ is the temperature of the surroundings,and $k$ is a constant. Integrating this differential equation gives $T(t) = T_0 + (T_{initial} - T_0)e^{-kt}$. This equation represents an exponential decay curve where the temperature $T$ asymptotically approaches the ambient temperature $T_0$ as time $t$ increases. Therefore,the curve in option $B$ correctly represents this cooling process.

$A$ block of metal is heated to a temperature much higher than the room temperature and allowed to cool in a room free from air currents. Which of the following curves correctly represents the rate of cooling?

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