Newton's law of cooling is a special case of

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(A) According to Stefan's law,the rate of heat loss $dQ/dt$ from a body at temperature $T$ to the surroundings at temperature $T_0$ is given by $dQ/dt

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Stefan's law

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(A) According to Stefan's law,the rate of heat loss $dQ/dt$ from a body at temperature $T$ to the surroundings at temperature $T_0$ is given by $dQ/dt = e \sigma A (T^4 - T_0^4)$.If the temperature difference $\Delta T = T - T_0$ is very small,we can write $T = T_0 + \Delta T$.Then $T^4 = (T_0 + \Delta T)^4 = T_0^4 (1 + \Delta T/T_0)^4$.Using binomial expansion,$T^4 \approx T_0^4 (1 + 4 \Delta T/T_0) = T_0^4 + 4 T_0^3 \Delta T$.Substituting this into the Stefan's law equation: $dQ/dt = e \sigma A (T_0^4 + 4 T_0^3 \Delta T - T_0^4) = 4 e \sigma A T_0^3 \Delta T$.Since $4 e \sigma A T_0^3$ is a constant,we get $dQ/dt \propto \Delta T$,which is Newton's law of cooling.Therefore,Newton's law of cooling is a special case of Stefan's law.

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