Three rods made of same material and having same cross-sectional area but different lengths 10,,cm ,

English

Gujarati

Hindi

10-2.Transmission of Heat

normal

Three rods made of the same material and having same cross-sectional area but different lengths $10\,\,cm$, $\,\,20 cm$ and $30\,\,cm$ are joined as shown. The temperature of the joint is ....... $^oC$

A

$20$

B

$23.7$

C

$16.4$

D

$18.2$

Solution

Let $\theta$ be the temperature of junction and $H_{1}, H_{2}$ and $H_{3}$ the heat currents.

Then

$H_{1}=H_2+H_{3}$

$\frac{30-\theta}{\left(\frac{30}{K A}\right)}=\frac{\theta-20}{\left(\frac{20}{K A}\right)}+\frac{\theta-10}{\left(\frac{30}{K A}\right)}$

or $2(30-\theta)=3(\theta-20)+3(2 \theta-20)$

or $\theta=16.36^{\circ} \mathrm{C} \approx 16.4^{\circ} \mathrm{C}$

Standard 11

Physics

Share

Similar Questions

Find Temperature difference between $B$ and $C$ ? (All rods are identical)

normal

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

On a cold morning, a metal surface will feel colder to touch than a wooden surface because

easy

(AIIMS-1998)

The end $A$ of a rod $AB$ of length $1\,m$ is maintained at $80\,^oC$ and the end $B$ at $0\,^oC.$ The temperature at a distance of $60\,\,c.m.$ from the end $A$ is……… $^oC$

medium

Three identical rods $AB$, $CD$ and $PQ$ are joined as shown. $P$ and $Q$ are mid points of $AB$ and $CD$ respectively. Ends $A, B, C$ and $D$ are maintained at $0^o C, 100^o C, 30^o C$ and $60^o C$ respectively. The direction of heat flow in $PQ$ is

normal