Two rods one made of copper and other made of steel of the same length and same cross sectional area are joined together. The thermal conductivity of copper and steel are 385 J s -1 K -1 m -1 and 50 J s -1 K -1 m -1 respectively. The free ends of copper and steel are held at 100° C and 0° C respectively. The temperature at the junction is, nearly:

Question

Two rods one made of copper and other made of steel of the same length and same cross sectional area are joined together. The thermal conductivity of copper and steel are 385 J s -1 K -1 m -1 and 50 J s -1 K -1 m -1 respectively. The free ends of copper and steel are held at 100° C and 0° C respectively. The temperature at the junction is, nearly: (A) 12° C (B) 50° C (C) 73° C (D) 88.5° C

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<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/230635e50c67d3151706e66fb4a05be0-.png" /> (Δ θ/Δ t )=(385 A (100-θ)/ℓ)=(50 A (θ-0)/ℓ) ⇒ 77(100-θ)=10 θ ⇒ 7700-77 θ=10 θ ⇒ 87 θ=7700 ⇒ θ=(7700/87)=88.5° C

$1 2^{\circ} C$

$5 0^{\circ} C$

$7 3^{\circ} C$

$88. 5^{\circ} C$

$\frac{Δ θ}{Δ t} = \frac{385 A ( 100 - θ )}{ℓ} = \frac{50 A ( θ - 0 )}{ℓ}$
$\Rightarrow 77 (100 - θ) = 10 θ$
$\Rightarrow 7700 - 77 θ = 10 θ$
$\Rightarrow 87 θ = 7700$
$\Rightarrow θ = \frac{7700}{87} = 88. 5^{\circ} C$

12∘C

50∘C

73∘C

88.5∘C

ΔtΔθ​=ℓ385A(100−θ)​=ℓ50A(θ−0)​ ⇒77(100−θ)=10θ ⇒7700−77θ=10θ ⇒87θ=7700 ⇒θ=877700​=88.5∘C

$1 2^{\circ} C$

$5 0^{\circ} C$

$7 3^{\circ} C$

$88. 5^{\circ} C$

$\frac{Δ θ}{Δ t} = \frac{385 A ( 100 - θ )}{ℓ} = \frac{50 A ( θ - 0 )}{ℓ}$
$\Rightarrow 77 (100 - θ) = 10 θ$
$\Rightarrow 7700 - 77 θ = 10 θ$
$\Rightarrow 87 θ = 7700$
$\Rightarrow θ = \frac{7700}{87} = 88. 5^{\circ} C$