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

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10-2.Transmission of Heat

hard

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 junction is......... $^oC$

$10.8$

$14.6$

$16.4$

$18.2$

Solution

Let $\theta$ be the temperature of junction, $\mathrm{H}_{1}$ $\mathrm{H}_{2}$ and $\mathrm{H}_{3}$ the heat currents. Then

$\mathrm{H}_{1}=\mathrm{H}_{2}+\mathrm{H}_{3}$

or $\frac{30-\theta}{\left(\frac{30}{\mathrm{KA}}\right)}=\frac{\theta-20}{\left(\frac{20}{\mathrm{KA}}\right)}+\frac{\theta-10}{\left(\frac{10}{\mathrm{KA}}\right)}$

or $2\left(30^{\circ}-\theta\right)=3(\theta-20)+6(\theta-10)$

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

Standard 11

Physics

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medium

Give definition, unit and dimensional formula of thermal conductivity.

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Which of the following statements is/are $CORRECT$ Correct option are

$(i)$ a body with large reflectivity is a poor emitter

$(ii)$ a brass tumbler feels much colder than a wooden tray on a chilly day

$(iii)$ the earth without its atmosphere would be inhospitably cold

$(iv)$ heating systems based on circulation of steam are more efficient in warming a building than those based on circulation of hot water

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Consider two insulating sheets with thermal resistances $R_1$ and $R_2$ as shown. The temperatures $\theta $ is

medium

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 junction is......... $^oC$

Solution

Similar Questions

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

Give definition, unit and dimensional formula of thermal conductivity.

There are two identical vessels filled with equal amounts of ice. The vessels are of different metals., If the ice melts in the two vessels in $20$ and $35$ minutes respectively, the ratio of the coefficients of thermal conductivity of the two metals is

Consider two insulating sheets with thermal resistances $R_1$ and $R_2$ as shown. The temperatures $\theta $ is

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