A metal sphere of radius 8 cm and mass 10 kg is heated to a temperature of $227^{0} C$ and is kept in a surrounding of $27^{0} C$ . If emissivity is 1 and specific heat is $90 cal / {kg}^{0} C$ , then initial rate of cooling is $(\frac{σπ}{J} = 4.2 \times 10^{- 8})$
Where $σ$ is stephen/botzmann constant and $J$ is mecanical equivalent of heat.

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$0 . 07^{0} C / s$

$0 . 01^{0} C / s$

$0 . 45^{0} C / s$

$0 . 25^{0} C / s$

answer is B.

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Detailed Solution

$ms \frac{dθ}{dt} = \frac{dQ}{dt} = eσA (T^{4} - T_{0}^{4})$

$\Rightarrow - \frac{dθ}{dt} = \frac{eσA (T^{4} - T_{0}^{4})}{ms} = \frac{4 {πr}^{2} eσ (T^{4} - T_{0}^{4})}{ms} \Rightarrow - \frac{dθ}{dt} = \frac{4 \times 3.14 \times 64 \times 10^{- 4} \times 5.67 \times 10^{- 8} \times (500^{4} - 300^{4})}{10 \times 90 \times 4.2} = 0 . 07^{0} C / s$