Two solid spheres of same material but diameters in the ratio of 5 : 4 are at temperatures 227^(@)Cand127^(@)C respectively. The temperature of the surrounding is 27^(@)C and Stefan's law holds. Calculate the ratio of rates of loss of heat of the two spheres?

Two solid spheres of same material but diameters in the ratio of 5 : 4

1.	Two solid spheres of same material but diameters in the ratio of 5 : 4 are at temperatures 227^(@)Cand127^(@)C respectively. The temperature of the surrounding is 27^(@)C and Stefan's law holds. Calculate the ratio of rates of loss of heat of the two spheres?
Answer» Solution :If `E_("net")` is the energy lost per second by UNIT SURFACE area, then `E_("net")=sigma(T^(4)-T_(0)^(4))` `therefore` Energy lost by the whole sphere in 1 sec = `4pir^(2)sigma(T^(4)-T_(0)^(4))` Now `("Rate of heat lost by the I sphere")/("Rate of heat lost by the II sphere")` = `(r_(1)^(2)(T_(1)^(4)-T_(0)^(4)))/(r_(2)^(2)(T_(2)^(4)-T_(0)^(4)))=(5/4)^(2)[(500^(4)-300^(4))/(400^(4)-300^(4))]=34/7`