A copper sphere is suspended in an evacuated chamber maintained at 300 K. The sphere is maintained at a constant temperature of 500 K by heating it electrically. A total of 210 W of electric power is needed to do it. When the surface of the copper sphere is completely blackened, 700 W is needed to maintain the same temperature of the sphere. Calculate the emissivity of copper.

Sol. Q = eσA(T base 2^4 – T base 1^4) For any body, 210 = eAσ[(500)^4 – (300)^4] For black body, 700 = 1 * Aσ[(500)^4 – (300)^4] Dividing 210/700 = e/1 ⇒ e = 0.3 Q/t = eAe(T base 2^4 – T base 1^4) ⇒ Q/At = 1 * 6 * 10^-8 [(300)^4 – (290)^4] = 6 * 10^-8 (81 * 10^8 – 70.7 * 10^8) = 6 * 10.3 Q/t = KA(θ base 1 – θ base 2)/l ⇒ Q/tA = K(θ base 1 – θ base 2)/l = K * 17/0.5 = 6 * 10.3 = K = 17/0.5 ⇒ K = 6 * 10.3 * 0.5/17 = 1.8