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Stefan-Boltzman's Law

Two solid sph...

Question

Two solid spheres, of radii $R_{1}$ and $R_{2}$ are made of the same material and have similar surface. The spheres are raised to the same temperature and then allowed to cool under identical conditions.Assuming Spheres to be perfect conductors of heat, their initial rates of loss of heat are

R_{1}^{2} / R_{2}^{2}

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R_{1} / R_{2}

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R_{2} / R_{1}

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R_{2}^{2} / R_{1}^{2}

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Solution

The correct option is A $R_{1}^{2} / R_{2}^{2}$
From stefan's law, we know that:
$Q = σ A T^{4} \times e$
where, area of sphere $A = 4 π R^{2}$
Here, temperature, thermal conductivity and emissivity of material are same.
So, we get the relation:
Initial rate of cooling is given as: $\frac{Q_{1}}{Q_{2}} = \frac{R_{1}^{2}}{R_{2}^{2}}$

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