Question

Three rods made of the same material and having the same cross- section have been joined as shown in the figure. Each rod is of the same length. The left and right ends are kept at 0°C and 90°C respectively. The temperature of the junction of the three rods will be

Answer 1

Answer:

Let θ

∘

C be the temperature at B. Let Q be the heat flowing per second from A to B on account of temperature difference by conductivity.

∴Q=

l

KA(90−θ)

...(i)

where k= thermal conductivity of the rod, A= Area of cross section of the rod, l= length of the rod. By symmetry, the same will be the case for heat flow from C to B.

∴ The heat flowing per second from B to D will be

2Q=

l

KA(θ−0)

....(ii)

Dividing Eq. (ii) by Eq. (i)

2=

90−θ

θ

⇒θ=60

∘

C.