Two metallic spheres (P ) and (Q ) are made of same material have same smoothness but the weight of (P ) is 8 times that of (Q ). If the two are heated to same temperature and left to cool, then the ratio of rate of cooling of (Q ) to that of (P ) is

Step-by-step solution

Given, weight of material (P ) is 8 times the weight of material (Q ). i.e., ( m_p=8 m_Q ) From stefan's law, the rate of heat radiation from an object is given by ( Q t =e A T^4 )...(i) where, (e= ) emissivity, ( = ) Stefan's constant (A= area and T= Temperature ) But, ( Q=m c T )...(ii) ( ) From Eqs. (i) and (ii), we get ( aligned m c T t & =e A T^4 T t & = e A T^4 m c (iii) aligned ) But, ( m= 4 3 r^3 ) ( r= ( 3 m 4 )^ 1 3 ) ( A=4 r^2=4 ( 3 m 4 )^ 2 3 )...(iv) ( ) From Eqs. (iii) and (iv), we get ( aligned & T t