Most Important Selected Qs for JEE AdvancedPhysicsThermal Properties of Matter
A solid sphere of radius =1 ~m has heat source throughout the volume such that heat is generated uniformly per unit volume inside it at a constant rate of 1.5 KW / m ^3 . At steady state the outer surface temperature is at 30^ C . Find the maximum temperature ( ^ C ) in the sphere at steady state. Thermal conductivity of this sphere =10 ~W / m ^ C . Assume that heat flows uniformly in radial direction.
Correct answer
55
Step-by-step solution
Consider a concentric smaller sphere of radius r within the given sphere Heat generated w 4 3 r^3 where w is heat generation rate per unit volume. w 4 3 r ^3= K 4 r ^2 (- dT dr ) dT =- w 3 ~K rdr T=- w 6 K r^2+C at r=R T = T ₀ C = T ₀+ w 6 ~K R ^2 T = T ₀+ W 6 ~K ( R ^2- r ^2 ) T = T _ when r =0 (at the center)