Three rods of same material, same area of cross-section but different lengths 10 cm , 20 cm and 30 cm are connected at a point as shown. What is temperature of junction O ?

Question

Three rods of same material, same area of cross-section but different lengths 10 cm , 20 cm and 30 cm are connected at a point as shown. What is temperature of junction O ? (A) 19.2° C (B) 16.4° C (C) 11.5° C (D) 22° C

Tardigrade Admin · Accepted Answer

Let temperature of junction be =θ Heat flowing to junction = heat out flowing (K A/30)(30-θ)=(K A/20)(θ-20)+(K A/10)(θ-10) ((30-θ)/3)=((θ-20)/2)+((θ-10)/1) ((30-θ)/3)=(θ-20+2 θ-20/2) 60-2 θ=9 θ-120 (180/11)=θ 16.36° C =θ

Q. Three rods of same material, same area of cross-section but different lengths $10 c m, 20 c m$ and $30 c m$ are connected at a point as shown. What is temperature of junction $O$ ?

$19. 2^{\circ} C$

$16. 4^{\circ} C$

$11. 5^{\circ} C$

$2 2^{\circ} C$

Q. Three rods of same material, same area of cross-section but different lengths 10cm,20cm and 30cm are connected at a point as shown. What is temperature of junction O ?

19.2∘C

16.4∘C

11.5∘C

22∘C

Let temperature of junction be =θ Heat flowing to junction = heat out flowing 30KA​(30−θ)=20KA​(θ−20)+10KA​(θ−10) 3(30−θ)​=2(θ−20)​+1(θ−10)​ 3(30−θ)​=2θ−20+2θ−20​ 60−2θ=9θ−120 11180​=θ 16.36∘C=θ

Q. Three rods of same material, same area of cross-section but different lengths $10 c m, 20 c m$ and $30 c m$ are connected at a point as shown. What is temperature of junction $O$ ?

$19. 2^{\circ} C$

$16. 4^{\circ} C$

$11. 5^{\circ} C$

$2 2^{\circ} C$