Two rectangular blocks A and B of different metals have the same length and same area of cross-section. They are kept in such a way that their cross-sectional areas are in contact. The temperature at one end of A is 100 ° C and that of B at the other end is 0 ° C . If the ratio of their thermal conductivity is 1:3 , then under steady-state, the temperature of the junction in contact will be

Question

Two rectangular blocks A and B of different metals have the same length and same area of cross-section. They are kept in such a way that their cross-sectional areas are in contact. The temperature at one end of A is 100 ° C and that of B at the other end is 0 ° C . If the ratio of their thermal conductivity is 1:3 , then under steady-state, the temperature of the junction in contact will be (A) 25 ° C (B) 50 ° C (C) 75 ° C (D) 100 ° C

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="Solution" src="https://cdn.tardigrade.in/q/nta/p-ppj5du6n7ryei1rd.jpg" /> It is given that (K1/K2)=(1/3) Let K1=K K2=3K The temperature of the junction in contact θ =(K1 θ 1 + K2 θ 2/K1 + K2) θ =(1 × 100 + 3 × 0/1 + 3)=(100/4) θ =25° C

$25^{\circ} C$

$50^{\circ} C$

$75^{\circ} C$

$100^{\circ} C$

It is given that $\frac{K _{1}}{K _{2}} = \frac{1}{3}$
Let $K_{1} = K & K_{2} = 3 K$
The temperature of the junction in contact
$θ = \frac{K _{1} θ _{1} + K _{2} θ _{2}}{K _{1} + K _{2}}$
$θ = \frac{1 \times 100 + 3 \times 0}{1 + 3} = \frac{100}{4}$
$θ = 2 5^{\circ} C$

25∘C

50∘C

75∘C

100∘C

It is given that K2​K1​​=31​ Let K1​=K&K2​=3K The temperature of the junction in contact θ=K1​+K2​K1​θ1​+K2​θ2​​ θ=1+31×100+3×0​=4100​ θ=25∘C

$25^{\circ} C$

$50^{\circ} C$

$75^{\circ} C$

$100^{\circ} C$

It is given that $\frac{K _{1}}{K _{2}} = \frac{1}{3}$
Let $K_{1} = K & K_{2} = 3 K$
The temperature of the junction in contact
$θ = \frac{K _{1} θ _{1} + K _{2} θ _{2}}{K _{1} + K _{2}}$
$θ = \frac{1 \times 100 + 3 \times 0}{1 + 3} = \frac{100}{4}$
$θ = 2 5^{\circ} C$