Seven identical rods of material of thermal conductivity k are connected as shown in Fig. All the rods are of identical length l and cross sectional area A If the one end B is kept at 100^@C and the other end is kept at 0^@C what would be the temperatures of the junctions C, D and E(theta_C,theta)D and theta_E) in the steady state?

Seven identical rods of material of thermal conductivity k are conne

1.	Seven identical rods of material of thermal conductivity k are connected as shown in Fig. All the rods are of identical length l and cross sectional area A If the one end B is kept at 100^@C and the other end is kept at 0^@C what would be the temperatures of the junctions C, D and E(theta_C,theta)D and theta_E) in the steady state?
Answer» `theta_Cgttheta_Egttheta_D` `theta_E=50^@C` and `theta_D=37.5^@C` `theta_E=50^@C`,`theta_C=62.5^@C` and `theta_D=37.5^@C` `theta_E=50^@C`,`theta_C=60^@C` and `theta_D=40^@C` Solution : This problem can be solved like electric current problem. `R_1`,`R_2`,`R_3`,`R_4`,`R_5`,`R_6` and `R_7` be the RATES of heat flow through AE,EB,AC,CD,CE,ED and DB, RESPECTIVELY. Since `R_1=R_2` `theta_E=50^@C` .(i) `R_5=R_6` `R_3=R_4+R_5=R_7`.(ii) `R_4+R_6=R_7` `(KA(theta_C-50))/(L)=(kA)/(l)(theta_C-50)+(kA)/(l)(theta_C-theta_D)=(kA)/(l)theta_D` `theta_C+theta_D=100` `2theta_C-2theta_D=50impliestheta_C=62.5^@C` `theta_D=37.5^@C` `theta_Cgttheta_Egttheta_D`