A wall is made of equally thick layers A and B of different materials. Thermal conductivity of A is twice that of B. In the steady state, the temperature difference across the wall is 36°C. The temperature difference across the layer A is

Question

A wall is made of equally thick layers A and B of different materials. Thermal conductivity of A is twice that of B. In the steady state, the temperature difference across the wall is 36°C. The temperature difference across the layer A is (A) 12 °C (B) 18 °C (C) 6 °C (D) 24 °C

Tardigrade Admin · Accepted Answer

Here, KA = 2KB, TA - TB = 36°C Let T is the temperature of the junction. As ((Δ T/Δ t))A=((Δ T/Δ t))B ∴ (KAA(TA-T)/x)=(KBA(T-TB)/x) 2KB(TA-T)=KB(T-TB) 2(TA-T)=T-TB Add (TA-T) on both sides, we get 3(TA-T)=TA-T+T-TB 3(TA-T)=TA-TB TA-T=(TA-TB/3) =(36/3)=12 °C ∴ Temperature difference across the layer A=TA-T=12 °C

Q. A wall is made of equally thick layers $A$ and $B$ of different materials. Thermal conductivity of $A$ is twice that of $B$ . In the steady state, the temperature difference across the wall is $3 6^{\circ} C$ . The temperature difference across the layer $A$ is

$12^{\circ} C$

$18^{\circ} C$

$6^{\circ} C$

$24^{\circ} C$

Q. A wall is made of equally thick layers A and B of different materials. Thermal conductivity of A is twice that of B. In the steady state, the temperature difference across the wall is 36∘C. The temperature difference across the layer A is

12∘C

18∘C

6∘C

24∘C

Q. A wall is made of equally thick layers $A$ and $B$ of different materials. Thermal conductivity of $A$ is twice that of $B$ . In the steady state, the temperature difference across the wall is $3 6^{\circ} C$ . The temperature difference across the layer $A$ is

$12^{\circ} C$

$18^{\circ} C$

$6^{\circ} C$

$24^{\circ} C$