Three rods of identical cross-section and len | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) The rods are identical,meaning they have the same length $(\ell)$ and area of cross-section $(A)$.Since the rods are joined in series,the rate of

Vedclass · Accepted Answer

$K_{1}: K_{3}=2: 3 ; K_{2}: K_{3}=2: 5$

Vedclass · Answer

(A) The rods are identical,meaning they have the same length $(\ell)$ and area of cross-section $(A)$.Since the rods are joined in series,the rate of heat flow (heat current) is the same for all rods in a steady state.Let the heat current be $H = \frac{\Delta Q}{\Delta t}$.$H = \frac{K_{1} A (100 - 70)}{\ell} = \frac{K_{2} A (70 - 20)}{\ell} = \frac{K_{3} A (20 - 0)}{\ell}$Simplifying the equation:$30 K_{1} = 50 K_{2} = 20 K_{3}$Dividing by $10$:$3 K_{1} = 5 K_{2} = 2 K_{3}$From $3 K_{1} = 2 K_{3}$,we get $\frac{K_{1}}{K_{3}} = \frac{2}{3}$ or $K_{1}: K_{3} = 2: 3$.From $5 K_{2} = 2 K_{3}$,we get $\frac{K_{2}}{K_{3}} = \frac{2}{5}$ or $K_{2}: K_{3} = 2: 5$.Thus,the correct relationship is $K_{1}: K_{3} = 2: 3$ and $K_{2}: K_{3} = 2: 5$.

Similar Questions

$A$ slab consists of two identical plates of copper and brass. The free face of the brass is at $0^{\circ} C$ and that of copper at $100^{\circ} C$. If the thermal conductivities of brass and copper are in the ratio $1: 4$,then the temperature of the interface is (in $^{\circ} C$)

$A$ metal rod of length $2\, m$ has cross-sectional areas $2A$ and $A$ as shown in the figure. The two ends are maintained at temperatures $100\,^{\circ}C$ and $70\,^{\circ}C$. The temperature of the junction point $C$ is ........ $^{\circ}C$.

$A$ rod of length $l$ with thermally insulated lateral surface is made of a material whose thermal conductivity $K$ varies as $K = C/T$,where $C$ is a constant. The ends are at temperatures $T_1$ and $T_2$. The heat current density is

The unit of thermal conductivity is

Vedclass Test Series

Exam Paper Generator

Online Exam Module