Two solid spheres of radii R_1 and R_2 are ma | vedclass

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(D) The rate of heat loss by radiation is given by Stefan-Boltzmann Law: $dQ/dt = e \sigma A (T^4 - T_0^4)$.Since the spheres are at the same temperat

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$R_2 / R_1$

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(D) The rate of heat loss by radiation is given by Stefan-Boltzmann Law: $dQ/dt = e \sigma A (T^4 - T_0^4)$.Since the spheres are at the same temperature $T$ and in the same environment $T_0$,the rate of heat loss is proportional to the surface area $A = 4 \pi R^2$.Thus,$dQ/dt \propto R^2$.The rate of cooling is defined as $dT/dt = (dQ/dt) / (mc)$,where $m$ is the mass and $c$ is the specific heat capacity.Mass $m = \rho V = \rho (4/3 \pi R^3)$,where $\rho$ is the density.Therefore,the rate of cooling $dT/dt \propto R^2 / R^3 = 1/R$.The ratio of the initial rates of cooling is $(dT/dt)_1 / (dT/dt)_2 = R_2 / R_1$.

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