Question

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

• A. $19.1\text{W}$
• B. $21.2\text{W}$
• C. $30\text{W}$
• D. $8\text{W}$

Answer 1

The correct option is B $21.2\text{W}$

Since the temperature of ball is constant,
Rate at which it is lossing heat = Rate at which heat is supplied to it.
Rate of heat loss $=\frac{dQ}{dt}=eA\sigma (T^4-T_s^4)$
$=0.3\times 4\pi (0.01{)}^2\times 5.67\times {10}^{-8}({1000}^4-{300}^4)$
$=21.2\text{watt}$
Therefore, electrical energy should be supplied at the same rate.