Heat and Thermal ExpansionHard

Question

A metallic sphere having radius 0.08 m and mass m = 10 kg is heated to a temperature of 227oC and suspended inside a box whose walls are at a temperature of 27oC. The maximum rate at which its temperature will fall is : - (Take e = 1, Stefan′s constant σ = 5.8 × 10-8 Wm-2 K-4 and specific heat of the metal s = 90 cal / kg / deg, J = 4.2 J / Calorie)

Options

A.0.055 oC/s
B.0.066 oC/s
C.0.044 oC/s
D.0.003 oC/s

Solution

From Stefan’s law of cooling :
eσA (T4 - T04) = ms
⇒ 1 × 5.8 × 10-8 × π × (0.082) × (5004 - 3004)
=10 × 90 × 4.2 × ⇒ = 0.067 oC/sFrom Stefan’s law of cooling :
eσA (T4 - T04) = ms
⇒ 1 × 5.8 × 10-8 × π × (0.082) × (5004 - 3004)
=10 × 90 × 4.2 × ⇒ = 0.067 oC/s

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