Two solidsphere of same matericalbut diameters in the raito of 5: 4 are at temperature 227^(@)Cand 127^(@)Crespectively. Thetemperatureof thesurroundingis 270^(@)Cand Stefan's lawholds . Calculatethe rates of heatradiation of thespheres ?

Two solidsphere of same matericalbut diameters in the raito of 5: 4 ar

1.	Two solidsphere of same matericalbut diameters in the raito of 5: 4 are at temperature 227^(@)Cand 127^(@)Crespectively. Thetemperatureof thesurroundingis 270^(@)Cand Stefan's lawholds . Calculatethe rates of heatradiation of thespheres ?
Answer» Solution :If `E_("net")` is the enegylostper secondby unitsurfacce area , then `E_("net") = sigma (T^(4) - T_(0)^(4))` `therefore ` Energy lostby the wholesphere in 1 sec ` = 4pi r^(2) sigma (T^(4) - T_(0)^(4))` Now `("Rateof heat lostby sphere I")/("Rateof heat lost by sphere II") =(r_(1)^(2)(T_(1)^(4) - T_(0)^(4)))/(r_(2)^(2)(T_(2)^(4) - T_(0)^(4))) = ((5)/(4))[(500^(4) - 300^(4))/(400^(4) - 300^(4))] = (34)/(7)`