Question

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

Answer: (A)

$\frac{K_{P} A \left[\right. 100 - \theta \left]\right.}{l}=\frac{K_{Q} A \left[\right. \theta \left]\right.}{l}$
$\therefore \frac{K_{p}}{K_{Q}}=\frac{2}{3}=\frac{\theta }{100 - \theta }$ or $\theta =40^\circ C$