Assuming Newton's law of cooling to be valid, | vedclass

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

Vedclass · Accepted Answer

$50$

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(B) According to Newton's law of cooling,the rate of heat loss is proportional to the temperature difference between the body and its surroundings: $P = K(T - T_s)$,where $K$ is a constant,$T$ is the temperature of the body,and $T_s$ is the temperature of the surroundings.In the first case,the body is at $T_1 = 50^{\circ} C$ and the surroundings are at $T_s = 20^{\circ} C$. The heater provides $P_1 = 100 \ W$ to maintain the steady state.$100 = K(50 - 20)$$100 = K 	imes 30$$K = \frac{100}{30} = \frac{10}{3} \ W/^{\circ} C$In the second case,the body is at $T_2 = 35^{\circ} C$ and the surroundings are at $T_s = 20^{\circ} C$. Let the required power be $P_2$.$P_2 = K(35 - 20)$$P_2 = K 	imes 15$Substituting the value of $K$:$P_2 = \left(\frac{100}{30}ight) 	imes 15$$P_2 = \frac{100}{2} = 50 \ W$.

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