Three rods of the same dimensions have thermal conductivities 3K,2K and K . They are arranged as shown, with their ends at 100° C,50° C and 0° C . The temperature of their junction is :-

Question

Three rods of the same dimensions have thermal conductivities 3K,2K and K . They are arranged as shown, with their ends at 100° C,50° C and 0° C . The temperature of their junction is :- <img class="img-fluid question-image" alt="Question" src="https://cdn.tardigrade.in/q/nta/p-avtkm5xsoslblgyq.jpg" /> (A) 75° C (B) (200/3)° C (C) 40° C (D) (100/3)° C

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="Solution" src="https://cdn.tardigrade.in/q/nta/p-avtkm5xsoslbxup1.jpg" /> R propto (1/ Thermal conductivity ) R1=(R/3),R2=(R/2),R3=R i=i1+i2 (100 - θ /R / 3)=(θ - 50/R / 2)+(θ - 0/R) 300-3θ =2θ -100+θ 6θ =400⇒ θ =(200/3) ° C

Q. Three rods of the same dimensions have thermal conductivities $3 K, 2 K$ and $K$ . They are arranged as shown, with their ends at $10 0^{\circ} C, 5 0^{\circ} C$ and $0^{\circ} C$ .
The temperature of their junction is :-

$7 5^{\circ} C$

$\frac{200}{3}^{\circ} C$

$4 0^{\circ} C$

$\frac{100}{3}^{\circ} C$

$R \propto \frac{1}{T h er ma l co n d u c t i v i t y}$
$R_{1} = \frac{R}{3}, R_{2} = \frac{R}{2}, R_{3} = R$
$i = i_{1} + i_{2}$
$\frac{100 - θ}{R /3} = \frac{θ - 50}{R /2} + \frac{θ - 0}{R}$
$300 - 3 θ = 2 θ - 100 + θ$
$6 θ = 400 \Rightarrow θ = \frac{200}{3}_^{^{\circ}} C$

Q. Three rods of the same dimensions have thermal conductivities 3K,2K and K . They are arranged as shown, with their ends at 100∘C,50∘C and 0∘C . The temperature of their junction is :-

75∘C

3200​∘C

40∘C

3100​∘C