Question

The temperature of filament of 100 watt electric lamp is 2727 degree c , calculate its emissivity if length of filament is 8 cm and its radius is 0.5 mm. please answer this as soon as possible :") thanks

Answer 1

$\text{The following parameters are given:-}$

$\text{Power}(P) = 100 \; W$

$\text{Temperature}(T) = 2727 \; ^{\circ} C$

$\text{Length of filament}(l) = 8 \; cm = 8 \times 10^{-2} \; m$

$\text{Radius}(r) = 0.5 \; mm = 0.5 \times 10^{-3} \; m$

$\text{Using Stephen's Law which states that:}$

$\boxed{P = eA\sigma T^4}$

$\text{We know that area}(A) = \pi dl$

$\implies P = e(\pi dl)\sigma T^4$

$\text{We know that }\sigma = 5.67 \times 10^{-8}$

$\implies 100 = e (3.14)(2 \times 0.5 \times 10^{-3})(8 \times 10^{-2})(5.67 \times 10^{-8})(2727)^4$

$\implies 100 = e (3.14)( 10^{-3})(45.36 \times 10^{-10})(2727)^4$

$\implies 100 = e (142.4304 \times 10^{-13})(2727)^4$

$\implies 100 = e (142.4304 \times 10^{-13})(55301963567841)$

$\implies 100 = e (7876680791753021 \times 10^{-13})$

$\implies 100 = e (787.67)$

$\implies e = \dfrac{100}{787.67}$

$\implies e = 0.126956$

$\implies \boxed{e \approx 0.1267}$