Question

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

• A. 2018.8 W
• B. 1018.8 W
• C. 956.8 W
• D. 0 W

Answer 1

The correct option is A 2018.8 W

Net heat lost by sphere per second $H_{\text{net}}=e\sigma A(T^4-T_0^4)$
where $T=$ temperature of sphere $=3000\text{K}$
$T_0=$ temperature of surrounding $=300\text{K}$
$\Rightarrow A=4\pi r^2=4\pi (0.01{)}^2$
To maintain constant temperature, power input required = net heat loss per second from the surface
$P_{\text{input}}=e\sigma A(T^4-T_0^4)$
$P_{\text{input}}=0.35\times 5.67\times {10}^{-8}\times 4\pi (0.01{)}^2\times ({3000}^4-{300}^4)$
$\approx 2019.7\text{W}$