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

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
$$\begin{gathered} \frac{\Delta Q}{\mathrm{\Delta }t}=eA\sigma \left(T^4-T_0^4\right) \\ \Rightarrow ms·\frac{\Delta T}{\mathrm{\Delta }t}=1\times 6\times {10}^{-8}\times 6\times 25\times {10}^{-4}\left({500}^4-{300}^4\right) \\ \Rightarrow \frac{\Delta T}{\mathrm{\Delta }t}=\frac{36\times 25\times \left({500}^4-{300}^4\right)\times {10}^{-12}}{400} \\ \Rightarrow \frac{\Delta T}{\mathrm{\Delta }t}=0.12°\mathrm{C}/\mathrm{s} \end{gathered}$$