Question

A cubic block of mass 1.0 kg and edge 5.0 cm is heated to ${227}^{0}C$. it is kept in an evacuated chamber maintained at ${27}^{0}c$ . 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 $400Jk{g}^{-1}{K}^{-4}$

Answer 1

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

$\therefore Emissivity,e=1$

Constant of Stefan, $\sigma =6\times 10-8W{m}^{-2}{K}^{-2}$

Cube surface area, $A=6\times 25\times {10}^{-4}$

Mass of the cube, $m=1kg$

Cube material has the specific heat capacity, $s=400Jk{g}^{-1}{K}^{-1}$

Cube temperature, $T_1=227+273=500K$

The surrounding temperature, $T_0=27+273=300K$

Heat’s rate of flow is shown as

$\to \frac{\Delta Q}{\Delta t}=eA\sigma (T^4-T_0^4)$

$ms\bullet \frac{\Delta T}{\Delta t}=1\times 6\times 10-8\times 6\times 25\times 10-4({500}^4-{300}^4)$

$\frac{\Delta T}{\Delta t}=0.12°C/s$