Question

A metallic prong consists of $4$ rods made of the same material, cross-sections and same lengths as shown. The three forked ends are kept at $100$ and the handle end is at $0$. The temperature of the junction is

• A. $25$
• B. $50$
• C. $60$
• D. $75$

Answer 1

Answer: (D)

$75$

Let the length of each fork be $l$ and cross-section area be $A$ and Coefficient of thermal conduction be $k$

Let the temperature at the junction be $T$.

Heat input from each of the hot forks to the junction is $H_h=-kA(T-100)/l$

Heat input from the cold fork is $H_c=-kAT/l$

In steady state, net heat accumulation at the junction = 0.

Thus, $3\times H_h+H_c=0\Rightarrow 3(T-100)+T=0\Rightarrow 4T=300$

Thus, $T=75$