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A cubical block of mass 1.0 kg and edge 5.0 cm is heated to 227°C. It is kept in an evacuated chamber maintained at 27°C. Assuming that the block emits radiation like a - Physics

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Question

A cubical block of mass 1.0 kg and edge 5.0 cm is heated to 227°C. It is kept in an evacuated chamber maintained at 27°C. Assuming that the block emits radiation like a blackbody, find the rate at which the temperature of the block will decrease. Specific heat capacity of the material of the block is 400 J Kg-1 K-1.

Solution

It is given that a cube behaves like a black body.

∴ Emissivity, e = 1

Stefan's constant, σ = 6 × 10−8 W/(m2 K4)

Surface area of the cube, A = 6 × 25 × 10−4

Mass of the cube, m = 1 kg

Specific heat capacity of the material of the cube, s = 400 J/(kg-K)

Temperature of the cube, T1 = 227 + 273 = 500 K

Temperature of the surrounding, T0 = 27 + 273 = 300 K

Rate of flow of heat is given by

`(DeltaQ)/(Delta)`=eAσ ( T4 -T0 4)

⇒ ms . `(DeltaT)/(Deltat)` = 1× 6 × 10 × 25 × 10-4 (5004 -3004)

`rArr (DeltaT)/(Deltat) = (36xx25xx(500^4 - 300^4)xx10^-12)/400`

⇒ `(DeltaT)/(Deltat)= 0.12^circ C/s`

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Solution A cubical block of mass 1.0 kg and edge 5.0 cm is heated to 227°C. It is kept in an evacuated chamber maintained at 27°C. Assuming that the block emits radiation like a Concept: Qualitative Ideas of Blackbody Radiation.
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