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.

Answer 1

The rate at which the temperature of the block will decrease is ΔTΔt = 0.12°C/s

Explanation:

• It is given in the question that a cube acts like a black body.
• Therefore, Emissivity, e = 1
• Constant of Stefan, σ = 6 × 10−8 W/(m2 K4)
• Cube has the surface area, A = 6 × 25 × 10−4
• Mass of the cube, m = 1 kg
• Cube material has the specific heat capacity, s = 400 J/(kg-K)
• Cube has the temperature, T1 = 227 + 273 = 500 K
• The surrounding temperature, T0 = 27 + 273 = 300 K
• Heat’s rate of flow is shown as
• ΔQΔt = eAσT4 - T04
• ⇒ms•ΔTΔt = 1 × 6 × 10-8 × 6 × 25 × 10-4 5004-3004
• ⇒ΔTΔt = 0.12°C/s