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(B) According to Newton's law of cooling,the rate of loss of heat is proportional to the temperature difference between the body and its surroundings.

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(B) According to Newton's law of cooling,the rate of loss of heat is proportional to the temperature difference between the body and its surroundings. This is given by the expression:$-\frac{dT}{dt} = k'(T - T_0)$where $k' = \frac{k}{ms}$ is a constant,$T$ is the temperature of the body,and $T_0$ is the temperature of the surroundings.Rearranging and integrating this differential equation:$\int \frac{dT}{T - T_0} = -\int k' dt$$\ln(T - T_0) = -k't + C$$T - T_0 = e^{-k't + C} = Ae^{-k't}$$T = T_0 + Ae^{-k't}$This equation represents an exponential decay of temperature $T$ towards the ambient temperature $T_0$ as time $t$ increases. At $t = 0$,$T$ is maximum,and as $t 	o \infty$,$T 	o T_0$. The graph that shows this exponential decay is graph $(b)$.

$A$ block of metal is heated to a temperature much higher than the room temperature and placed in an evacuated cavity. Which curve correctly represents the rate of cooling? ($T$ is the temperature of the block and $t$ is the time.)

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