(C) Let $A_1$ and $A_2$ be the cross-sectional areas of the inner cylinder and the outer shell respectively.$A_1 = \pi R^2$$A_2 = \pi (2R)^2 - \pi R^2

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

(C) Let $A_1$ and $A_2$ be the cross-sectional areas of the inner cylinder and the outer shell respectively.$A_1 = \pi R^2$$A_2 = \pi (2R)^2 - \pi R^2 = 3\pi R^2$Total area $A = A_1 + A_2 = 4\pi R^2$.Since the two ends are at different temperatures and the system is in a steady state,the heat flow through both parts occurs in parallel.The equivalent thermal resistance $R_{eq}$ is given by $\frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2}$.Using $R = \frac{l}{kA}$,we have $\frac{kA}{l} = \frac{k_1 A_1}{l} + \frac{k_2 A_2}{l}$.Substituting the values:$k(4\pi R^2) = k_1(\pi R^2) + k_2(3\pi R^2)$$4k = k_1 + 3k_2$$k = \frac{k_1 + 3k_2}{4}$

Class 11 Physics 10-2.Heat Transfer Thermal Resistance and it's Combination

Difficult

$A$ cylinder of radius $R$ made of a material of thermal conductivity $k_1$ is surrounded by a cylindrical shell of inner radius $R$ and outer radius $2R$ made of a material of thermal conductivity $k_2$. The two ends of the combined system are maintained at different temperatures. There is no loss of heat from the cylindrical surface and the system is in steady state. The effective thermal conductivity of the system is

A
$k_1 + k_2$
B
$\frac{k_1 k_2}{k_1 + k_2}$
C
$\frac{1}{4}(k_1 + 3k_2)$
D
$\frac{1}{4}(3k_1 + k_2)$

Explore More

Browse All

Question Bank

All Subjects

Class 11 Questions

Class 11

Physics Questions

Chapter

10-2.Heat Transfer

Subtopic

Thermal Resistance and it's Combination

$A$ wall has two layers $A$ and $B,$ each made of different material. Both the layers have the same thickness. The thermal conductivity for $A$ is twice that of $B$ and under steady condition,the temperature difference across the wall is $36\,^{\circ}C.$ The temperature difference across the layer $A$ is....... $^{\circ}C$

Difficult

View Solution

Two metal rods are arranged as shown in the figure. Their thermal conductivities are $K_1$ and $K_2$. What is their equivalent thermal conductivity?

Medium

View Solution

Six identical conducting rods are joined as shown. The ends $A$ and $D$ are maintained at $200\,^{\circ}C$ and $20\,^{\circ}C$ respectively. No heat is lost to the surroundings. The temperature of the junction $C$ will be ........ $^{\circ}C$.

Difficult

View Solution

$A$ wall consists of alternating blocks of length $d$ and coefficients of thermal conductivity $K_{1}$ and $K_{2}$ respectively,as shown in the figure. The cross-sectional areas of the blocks are the same. The equivalent coefficient of thermal conductivity of the wall between the left and right sides is

MediumNEET 2017

View Solution

Two rods of same length and material transfer a given amount of heat in $12 \ s$,when they are joined end to end. But when they are joined along their lengths (parallel combination),then they will transfer the same amount of heat under the same conditions in time $t = \dots \ s$.

Medium

View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial

For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free

For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo

Similar Questions

Two metal rods are arranged as shown in the figure. Their thermal conductivities are $K_1$ and $K_2$. What is their equivalent thermal conductivity?

Six identical conducting rods are joined as shown. The ends $A$ and $D$ are maintained at $200\,^{\circ}C$ and $20\,^{\circ}C$ respectively. No heat is lost to the surroundings. The temperature of the junction $C$ will be ........ $^{\circ}C$.

Two rods of same length and material transfer a given amount of heat in $12 \ s$,when they are joined end to end. But when they are joined along their lengths (parallel combination),then they will transfer the same amount of heat under the same conditions in time $t = \dots \ s$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module