Question

The emissivity of tungsten is approximately $0.35$. A tungsten sphere having $1\text{cm}$ radius is suspended within a large evacuated enclosure whose walls are at $300\text{K}$. Find the power input required to maintain the sphere at a temperature of $3000\text{K}$ if heat conduction along the support is neglected. $\sigma =5.67\times {10}^{-8}\text{SI units}$.

• A. $1050\text{W}$
• B. $750\text{W}$
• C. $2019\text{W}$
• D. $3500\text{W}$

Answer 1

The correct option is C $2019\text{W}$

Rate of heat loss by sphere
$\frac{dQ}{dt}=eA\sigma (T^4-T_0^4)$
Given, $e=0.35,A=4\pi (0.01{)}^2,T_0=300K,T=3000K$
For maintaining the same temperature of sphere,
Power input $P=eA\sigma (T^4-T_0^4)$
$\Rightarrow P=0.35\times 4\pi \times (0.01{)}^2\times 5.67\times {10}^{-8}\times [(3000{)}^4-(300{)}^4]$
$\Rightarrow P\approx 2019\text{W}$
Thus, option (c) is the correct answer.