Two solid spheres of same ,naterial but diameters in the ratio of 5 : 4 are at temperatures `227^(0) and 127^(0)` C respectively. The temperature of the surrounding is `27^(0)` c and Stefan's law holds. Calculate the ratio of rates of loss of heat of the two spheres?

Explanation

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 =
`4 pi r^(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)`