Two different rods A and B are kept as shown in the figure. The variation of temperature of different cross-sections is plotted in the graph shown in the figure. Find the ratio of thermal conductivities of B to A.

Question

Two different rods A and B are kept as shown in the figure. <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/24383d9ad9d16c04f7a6856ff47105ad-.png" /> The variation of temperature of different cross-sections is plotted in the graph shown in the figure. Find the ratio of thermal conductivities of B to A. (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

∵((Δ Q/Δ t))A=((Δ Q/Δ t))B ∴ (-KA A(100-70)/30)=(KB A(70-35)/70) ⇒ KA=(KB/2) ⇒ (KB/KA)=2

Q. Two different rods $A$ and $B$ are kept as shown in the figure.

The variation of temperature of different cross-sections is plotted in the graph shown in the figure. Find the ratio of thermal conductivities of $B$ to $A$ .

$∵ (\frac{Δ Q}{Δ t})_{A} = (\frac{Δ Q}{Δ t})_{B}$
$∴ \frac{- K _{A} A ( 100 - 70 )}{30} = \frac{K _{B} A ( 70 - 35 )}{70}$
$\Rightarrow K_{A} = \frac{K _{B}}{2}$
$\Rightarrow \frac{K _{B}}{K _{A}} = 2$

Q. Two different rods A and B are kept as shown in the figure. The variation of temperature of different cross-sections is plotted in the graph shown in the figure. Find the ratio of thermal conductivities of B to A.

∵(ΔtΔQ​)A​=(ΔtΔQ​)B​ ∴30−KA​A(100−70)​=70KB​A(70−35)​ ⇒KA​=2KB​​ ⇒KA​KB​​=2

Q. Two different rods $A$ and $B$ are kept as shown in the figure.

The variation of temperature of different cross-sections is plotted in the graph shown in the figure. Find the ratio of thermal conductivities of $B$ to $A$ .

$∵ (\frac{Δ Q}{Δ t})_{A} = (\frac{Δ Q}{Δ t})_{B}$
$∴ \frac{- K _{A} A ( 100 - 70 )}{30} = \frac{K _{B} A ( 70 - 35 )}{70}$
$\Rightarrow K_{A} = \frac{K _{B}}{2}$
$\Rightarrow \frac{K _{B}}{K _{A}} = 2$