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A small object is placed at the centre of a large evacuated hollow spherical container. Assume that the container is maintained at 0 K. At time t = 0, the temperature of the object is 200 K. The temperature of the object become 100 K at t = t₁ and 50 K at t = t₂. Assume the object and the container to be ideal black bodies. The heat capacity of the object does not depend on temperature. The ratio (t₂/t₁) is_____.

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answer is 9.

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Detailed Solution

$σ A e (T^{4} O^{4}) = m s \frac{d T}{d t}; \to \int \frac{d T}{T^{4}} \infty \int d t$
$T_{1} = 100 k \frac{1}{T_{0}^{3}} - \frac{1}{T_{1}^{3}} = k t_{1}$
$T_{2} = 50 k \frac{1}{T_{0}^{3}} - \frac{1}{T_{2}^{3}} k t_{2} \frac{t_{2}}{t_{1}} = 9$

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