A block of metal is heated to a temperature m | vedclass

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(B) According to Newton's law of cooling,the rate of cooling 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 cooling is proportional to the temperature difference between the body and its surroundings.$ - \frac{d	heta}{dt} \propto (	heta - 	heta_0) $$ - \frac{d	heta}{dt} = \alpha (	heta - 	heta_0) $,where $\alpha$ is a constant.Integrating this differential equation:$ \int_{	heta_i}^{	heta} \frac{d	heta}{(	heta - 	heta_0)} = - \alpha \int_{0}^{t} dt $$ \ln(	heta - 	heta_0) - \ln(	heta_i - 	heta_0) = - \alpha t $$ 	heta = 	heta_0 + (	heta_i - 	heta_0) e^{-\alpha t} $This relation shows that the temperature of the body decreases exponentially with time from the initial temperature $	heta_i$ to the ambient temperature $	heta_0$. Therefore,the curve representing this exponential decay is the correct one,which corresponds to curve $B$.

$A$ 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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