A slab consists of two parallel layers of copper and brass of the same thickness and having thermal conductivities in the ratio 1:4 . If the free face of brass is at 100 ° C and that of copper at 0 ° C , the temperature of the interface is

Question

A slab consists of two parallel layers of copper and brass of the same thickness and having thermal conductivities in the ratio 1:4 . If the free face of brass is at 100 ° C and that of copper at 0 ° C , the temperature of the interface is (A) 80° C (B) 20° C (C) 60° C (D) 40° C

Tardigrade Admin · Accepted Answer

We know that (d Q/d t)=(K A ((θ )2 - (θ )1)/d) As slabs are in series, therefore ⇒ K1(θ1-θ mathrmC)=K2(θ mathrmC-θ2) ⇒ 4K(100 - θ )=K(θ - 0) ⇒ 400-4θ =θ ⇒ θ =80° C

Q. A slab consists of two parallel layers of copper and brass of the same thickness and having thermal conductivities in the ratio $1 : 4$ . If the free face of brass is at $100^{^{\circ}} C$ and that of copper at $0^{^{\circ}} C$ , the temperature of the interface is

$8 0^{\circ} C$

$2 0^{\circ} C$

$6 0^{\circ} C$

$4 0^{\circ} C$

We know that $\frac{d Q}{d t} = \frac{K A ( ( θ ) _{2} - ( θ ) _{1} )}{d}$
As slabs are in series, therefore
$\Rightarrow K_{1} (θ_{1} - θ_{C}) = K_{2} (θ_{C} - θ_{2})$
$\Rightarrow 4 K (100 - θ) = K (θ - 0)$
$\Rightarrow 400 - 4 θ = θ$
$\Rightarrow θ = 8 0^{\circ} C$

Q. A slab consists of two parallel layers of copper and brass of the same thickness and having thermal conductivities in the ratio 1:4 . If the free face of brass is at 100∘C and that of copper at 0∘C , the temperature of the interface is

80∘C

20∘C

60∘C

40∘C