Three rods A, B and C of thermal conductiviti | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Let $R_A, R_B$ and $R_C$ be the thermal resistances of rods $A, B$ and $C$ respectively. The thermal resistance is given by $R = \frac{l}{KA}$.$R_

Vedclass · Accepted Answer

$20$

Vedclass · Answer

(B) Let $R_A, R_B$ and $R_C$ be the thermal resistances of rods $A, B$ and $C$ respectively. The thermal resistance is given by $R = \frac{l}{KA}$.$R_A = \frac{2l}{KA}$$R_B = \frac{l}{(2K)(2A)} = \frac{l}{4KA}$$R_C = \frac{l}{(4K)(2A)} = \frac{l}{8KA}$Let $	heta$ be the temperature of the junction. The thermal currents flowing towards the junction must sum to zero (Kirchhoff's junction law for heat flow):$\frac{100 - 	heta}{R_A} + \frac{50 - 	heta}{R_B} + \frac{0 - 	heta}{R_C} = 0$Substituting the values of resistances:$\frac{100 - 	heta}{2l/KA} + \frac{50 - 	heta}{l/4KA} + \frac{0 - 	heta}{l/8KA} = 0$$\frac{KA}{l} \left[ \frac{100 - 	heta}{2} + 4(50 - 	heta) - 8	heta ight] = 0$$50 - 0.5	heta + 200 - 4	heta - 8	heta = 0$$250 = 12.5	heta$$	heta = \frac{250}{12.5} = 20^{\circ}C$

Similar Questions

Three rods of the same material and same cross-sectional area,but different lengths $10 \, cm$,$20 \, cm$,and $30 \, cm$,are connected at a junction $O$ as shown in the figure. What is the temperature of the junction $O$ in $^{\circ} C$?

In a composite rod,two rods of different lengths and the same cross-sectional area are joined end to end. If $K$ is the equivalent coefficient of thermal conductivity of the composite rod,then $\left( \frac{\ell_1 + \ell_2}{K} \right)$ is equal to:

Six identical conducting rods are joined as shown in the figure. Points $A$ and $D$ are maintained at temperatures of $200^oC$ and $20^oC$ respectively. The temperature of junction $B$ will be ....... $^oC$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module