Question

Two solid nuclear fueled pellets contain the exact same volume (3.14 cubic centimeters). Both pellets have the same max internal temperature and same surface temperatures Ti and Ts) pellet provides the most power; prove with derived equations. Ti Ti Ts r-,909cm r-1cm height-1cm

Answer 1

Power proportionalto Surface area P_cy/P_sphere = 2 pi rh + 2 pi r^2/4 pi r^2_1 = rh + r^2/2 r^2_1 = rh + r^2/2 (3r^2 h/4)^1/3 = 1 times 1 + 1/2 [3/4 times 1 times 1]^1/3 P_cy/P_sphere = 11/10 therefore P_cy > P_sphere therefore Cylinder provides more 4/3 pi r^3_1 = pi r^2 h r^3_1 = 3r^2 h/4 r_1 = (3r^2 h/4)^1/3