#### 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/(m^{2} K^{4})

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,* **T*_{1} = 227 + 273 = 500 K

Temperature of the surrounding,* **T*_{0} = 27 + 273 = 300 K

Rate of flow of heat is given by

`(DeltaQ)/(Delta)`=eAσ ( T^{4 }-T_{0} ^{4})

⇒ ms . `(DeltaT)/(Deltat)` = 1× 6 × 10 × 25 × 10^{-4 }(500^{4} -300^{4})

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

⇒ `(DeltaT)/(Deltat)= 0.12^circ C/s`