Two black spheres P & Q have radii in the ratio 4: 3 . The wavelength of maximum intensity of radiation are in the ratio 4: 5 respectively. The ratio of radiated power by P to Q is

Step-by-step solution

Wien's Displacement Law relates temperature and peak wavelength as _ max T = b , so T 1/ _ max . Given _ max,P / _ max,Q = 4/5 , we find T_P/T_Q = _ max,Q / _ max,P = 5/4 . The Stefan-Boltzmann Law gives radiated power P = A T^4 . For spheres, A = 4 R^2 , so P R^2 T^4 . The power ratio is then P_P/P_Q = (R_P/R_Q)^2 (T_P/T_Q)^4 . Substituting R_P/R_Q = 4/3 and T_P/T_Q = 5/4 : P_P/P_Q = (4/3)^2 (5/4)^4 = (16/9)(625/256) Simplifying yields P_P/P_Q = 625/144 .