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 ° C and at one end of Q is 0 ° C , then the temperature of the interface is

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 ° C and at one end of Q is 0 ° C , then the temperature of the interface is (A) 40 ° C (B) 50° C (C) 60° C (D) 70° C

Tardigrade Admin · Accepted Answer

(KP A [. 100 - θ ]./l)=(KQ A [. θ ]./l) ∴ (Kp/KQ)=(2/3)=(θ /100 - θ ) or θ =40° C

Q. 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

$40^{\circ} C$

$5 0^{\circ} C$

$6 0^{\circ} C$

$7 0^{\circ} C$

$\frac{K _{P} A [ 100 - θ ]}{l} = \frac{K _{Q} A [ θ ]}{l}$
$∴ \frac{K _{p}}{K _{Q}} = \frac{2}{3} = \frac{θ}{100 - θ}$ or $θ = 4 0^{\circ} C$

Q. 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∘C and at one end of Q is 0∘C , then the temperature of the interface is

40∘C

50∘C

60∘C

70∘C