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(D) According to Newton's Law of Cooling,the rate of heat loss is proportional to the temperature difference between the body and its surroundings: $\

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$20$

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(D) According to Newton's Law of Cooling,the rate of heat loss is proportional to the temperature difference between the body and its surroundings: $\frac{dQ}{dt} = k(	heta - 	heta_0)$.Given: $	heta_0 = 20^{\circ}C$.For the first case: $	heta_1 = 80^{\circ}C$ and $\frac{dQ_1}{dt} = 60 \, cal/sec$.Substituting these values: $60 = k(80 - 20) = 60k$,which implies $k = 1 \, cal/(sec \cdot ^{\circ}C)$.For the second case: $	heta_2 = 40^{\circ}C$.Calculating the rate of heat loss: $\frac{dQ_2}{dt} = k(40 - 20) = 1 	imes 20 = 20 \, cal/sec$.

$A$ liquid is filled in a container and placed in a room at a temperature of $20^{\circ}C$. When the temperature of the liquid is $80^{\circ}C$,it loses heat at a rate of $60 \, cal/sec$. Find the rate of heat loss when the temperature of the liquid is $40^{\circ}C$ in $cal/sec$.

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