(A) In steady state,the rate of heat flow through both sections is the same.Let $T$ be the temperature at the interface.The rate of heat flow $H$ is g

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

$\frac{K_1 l_2 T_1 + K_2 l_1 T_2}{K_1 l_2 + K_2 l_1}$

(A) In steady state,the rate of heat flow through both sections is the same.Let $T$ be the temperature at the interface.The rate of heat flow $H$ is given by $H = \frac{KA(T_{high} - T_{low})}{l}$.For the first section: $H = \frac{K_1 A(T_1 - T)}{l_1}$.For the second section: $H = \frac{K_2 A(T - T_2)}{l_2}$.Equating the two rates: $\frac{K_1 A(T_1 - T)}{l_1} = \frac{K_2 A(T - T_2)}{l_2}$.$\frac{K_1(T_1 - T)}{l_1} = \frac{K_2(T - T_2)}{l_2}$.$K_1 l_2(T_1 - T) = K_2 l_1(T - T_2)$.$K_1 l_2 T_1 - K_1 l_2 T = K_2 l_1 T - K_2 l_1 T_2$.$K_1 l_2 T_1 + K_2 l_1 T_2 = T(K_1 l_2 + K_2 l_1)$.$T = \frac{K_1 l_2 T_1 + K_2 l_1 T_2}{K_1 l_2 + K_2 l_1}$.

Class 11 Physics 10-2.Heat Transfer Heat Conduction and Thermal Conductivity

Medium

One end of a thermally insulated rod is kept at a temperature $T_1$ and the other at $T_2$. The rod is composed of two sections of length $l_1$ and $l_2$ and thermal conductivities $K_1$ and $K_2$ respectively. The temperature at the interface of the two sections is

AIEEE 2007 All AIEEE

A
$\frac{K_1 l_2 T_1 + K_2 l_1 T_2}{K_1 l_2 + K_2 l_1}$
B
$\frac{K_2 l_1 T_1 + K_1 l_2 T_2}{K_2 l_1 + K_1 l_2}$
C
$\frac{K_1 l_1 T_1 + K_2 l_2 T_2}{K_1 l_1 + K_2 l_2}$
D
$\frac{K_2 l_2 T_1 + K_1 l_1 T_2}{K_1 l_1 + K_2 l_2}$

Explore More

Browse All

Question Bank

All Subjects

Class 11 Questions

Class 11

Physics Questions

Chapter

10-2.Heat Transfer

Subtopic

Heat Conduction and Thermal Conductivity

Previous Year

AIEEE 2007 Paper All AIEEE years →

The outer faces of a rectangular slab made of equal thickness of iron and brass are maintained at $100^{\circ} C$ and $0^{\circ} C$ respectively. The temperature at the interface is ........... $^{\circ} C$ (Thermal conductivity of iron and brass are $0.2$ and $0.3$ respectively.)

Easy

View Solution

Mud houses are cooler in summer and warmer in winter because

Easy

View Solution

$A$ heat source at $T_1 = 10^3\, K$ is connected to another heat reservoir at $T_2 = 10^2\, K$ by a copper slab which is $1\, m$ thick. Given that the thermal conductivity of copper is $0.1\, W\, K^{-1}\, m^{-1}$,the energy flux through it in the steady state is ........... $W\, m^{-2}$.

DifficultJEE MAIN 2019

View Solution

$A$ cylindrical copper rod of length $2 \,m$ and cross-sectional area $2 \,cm^2$ is insulated at its curved surface. One end of the rod is maintained in a steam chamber at $100^{\circ} C$ and the other is maintained in ice at $0^{\circ} C$. The thermal conductivity of copper is $386 \,Js^{-1} \,m^{-1} {}^{\circ} C^{-1}$. Find the temperature at a point which is at a distance of $120 \,cm$ from the colder end. (in $^{\circ} C$)

DifficultAP EAMCET 2020

View Solution

Two sheets of thickness $d$ and $2d$ and the same area are touching each other on their faces. The temperatures $T_A$,$T_B$,and $T_C$ shown are in a geometric progression with a common ratio $r = 2$. Then,the ratio of the thermal conductivity of the thinner sheet to the thicker sheet is:

Difficult

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

One end of a thermally insulated rod is kept at a temperature $T_1$ and the other at $T_2$. The rod is composed of two sections of length $l_1$ and $l_2$ and thermal conductivities $K_1$ and $K_2$ respectively. The temperature at the interface of the two sections is

Similar Questions

The outer faces of a rectangular slab made of equal thickness of iron and brass are maintained at $100^{\circ} C$ and $0^{\circ} C$ respectively. The temperature at the interface is ........... $^{\circ} C$ (Thermal conductivity of iron and brass are $0.2$ and $0.3$ respectively.)

Mud houses are cooler in summer and warmer in winter because

$A$ heat source at $T_1 = 10^3\, K$ is connected to another heat reservoir at $T_2 = 10^2\, K$ by a copper slab which is $1\, m$ thick. Given that the thermal conductivity of copper is $0.1\, W\, K^{-1}\, m^{-1}$,the energy flux through it in the steady state is ........... $W\, m^{-2}$.

Two sheets of thickness $d$ and $2d$ and the same area are touching each other on their faces. The temperatures $T_A$,$T_B$,and $T_C$ shown are in a geometric progression with a common ratio $r = 2$. Then,the ratio of the thermal conductivity of the thinner sheet to the thicker sheet is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module