Question

A spherical ball of radius $1\text{cm}$ coated with a metal having emissivity $e=0.3$ is maintained at $1000\text{K}$ temperature and suspended in a vaccum chamber whose walls are maintained at $300\text{K}$. Find the rate at which electrical energy is to be supplied to the ball to keep its temperature constant. $[\sigma =5.67\times {10}^{-8}\text{W}{\text{m}}^{-2}{\text{K}}^{-4}]$

• A. $56.1\text{W}$
• B. $72\text{W}$
• C. $122\text{W}$
• D. $21.19\text{W}$

Answer 1

The correct option is D $21.19\text{W}$

Rate of heat radiated :
$\frac{dQ}{dt}=Ae\sigma (T^4-{T_0}^4)$
We know that, for constant temperature,
Rate of heat radiated = Rate of heat supplied
$\Rightarrow \frac{dQ}{dt}=0.3\times (4\times 3.14\times {0.01}^2)\times 5.67\times \left({10}^{-8}\right)\times [{1000}^4-{300}^4]$
$=21.19\text{W}$
Thus, option (d) is the correct answer.