An iron cube , of edge10 cm ,painted black is at a temperatureof 127^(@) C keptin aroom of tempeature27^(@)C. Ifthe densityand specific heat capacityof ironbe 7600 kg//m^(2)and 470 J// Kg - K , findthe initial rate of coolingof the cube.

An iron cube , of edge10 cm ,painted black is at a temperatureof 127^(

1.	An iron cube , of edge10 cm ,painted black is at a temperatureof 127^(@) C keptin aroom of tempeature27^(@)C. Ifthe densityand specific heat capacityof ironbe 7600 kg//m^(2)and 470 J// Kg - K , findthe initial rate of coolingof the cube.
Answer» Solution :Here , area `A = 6a^(2) ` and volume`V = a^(3) , a= 10 xx 10^(2)m ,e= 1 ` ( `because` the surfaceis painted black ). `rho = 7600 kg // m^(3) , s = 470 J.Kg - K, T = 400 K and T_(0) = 300K`the rate of cooling of a hot bodyis given by` - (dT)/(dt) = (Ae sigma)/(rho Vs)(T^(4) - T_(0)^(4))= (6a^(2) sigma)/( rhoa^(3)s) (T^(4) - T_(0)^(4))` `= (6 xx 5.67 xx 10^(-8) W (400^(4) - 300^(4))K^(4))/((7600(kg)/(m^(3)))((470J)/(Kg - K))m^(2) - K^(4) (10 xx 10^(-2) m))=16.67 xx 10^(-3) K//s`