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

Question

Six identical conducting rods are joined as shown in figure. Points A and D are maintained at temperatures 200° C and 20° C, respectively. The temperature of junction B will be (A) 120° C (B) 100° C (C) 140° C (D) 80° C

Tardigrade Admin · Accepted Answer

Let the thermal resistance of each rod be

R

.

The two resistances connected along two paths from

B

to

C

are equivalent to

2 R

each and their parallel combination is

R

. Effective thermal resistance between

B

and

D = 2 R

Temperature of interface

θ = \frac{R _{1} θ _{2} + R _{2} θ _{1}}{R _{1} + R _{2}}

θ = \frac{R \times 20 + 2 R \times 200}{R + 2 R} = \frac{420}{3} = 14 0^{\circ} C

Q. Six identical conducting rods are joined as shown in figure. Points $A$ and $D$ are maintained at temperatures $20 0^{\circ} C$ and $2 0^{\circ} C$ , respectively. The temperature of junction $B$ will be

$12 0^{\circ} C$

$10 0^{\circ} C$

$14 0^{\circ} C$

$8 0^{\circ} C$

Q. Six identical conducting rods are joined as shown in figure. Points A and D are maintained at temperatures 200∘C and 20∘C, respectively. The temperature of junction B will be

120∘C

100∘C

140∘C

80∘C

Q. Six identical conducting rods are joined as shown in figure. Points $A$ and $D$ are maintained at temperatures $20 0^{\circ} C$ and $2 0^{\circ} C$ , respectively. The temperature of junction $B$ will be

$12 0^{\circ} C$

$10 0^{\circ} C$

$14 0^{\circ} C$

$8 0^{\circ} C$