Question

Two rods P and Q of same length and same diameter having thermal conductivity ratio 2 : 3 joined end to end. If temperature at one end of P is ${100}^{\circ }C$ and at one and of Q $0^{\circ }C$, then the temperature of the interface is

• A. ${40}^{\circ }C$
• B. ${50}^{\circ }C$
• C. ${60}^{\circ }C$
• D. ${70}^{\circ }C$

Answer 1

The correct option is A ${40}^{\circ }C$

Let the temperature of interface of both the rod is $T$.
So heat flow rate will be: $\frac{Q}{t}=\frac{KA\Delta T}{L}$
So heat will flow from higher temperature to lower, hence at steady state we equate both of them to find the common intermediate temperature $T$.

$\frac{K_p(100-T)}{L}=\frac{K_q(T-0)}{L}$

It is given that: $\frac{K_p}{K_q}=\frac{2}{3}$

So, on putting in above equation we find:

$\frac{2}{3}(100-T)=T$
$\Rightarrow T={40}^{0}C$