Three rods of equal length L and equal cross-sectional area A are… - Vidyadip

Question

Three rods of equal length $L$ and equal cross-sectional area $A$ are connected in series. The thermal conductivities of their substances are $K , 2 K$ and $1.5 K.$ If the temperature of the open ends of the first and last rods are $200^{\circ} C$ and $18^{\circ} C$ then calculate the temperature at both the junctions whereas the radiation of heat loss is negligible.

✓

Answer

Suppose the temperature at B and C junction $T _1$ and $T _2$ respectively. Since the loss due to radiation is negligible, therefore, the rate of heat flow in the entire system will be the same in the steady state, hence

$\begin{array}{l}H_1=\frac{KA\left(200-T_1\right)}{L}\ldots\ldots (1) \\H_2=\frac{2 KA\left(T_1-T_2\right)}{L}\ldots\ldots (2) \\H_3=\frac{1.5 KA\left(T_2-18\right)}{L}\ldots\ldots (3) \\H_1=H_2=H_3 \\\therefore \quad \frac{KA\left(200-T_1\right)}{L}=\frac{2 KA\left(T_1-T_2\right)}{L} \\=\frac{(1.5 K) A\left(T_2-18\right)}{L} \\\text { or } \quad 200-T_1=2 T_1-2 T_2=1.5 T_2-27\end{array}$
Taking first two terms
$200-T_1=2 T_1-2 T_2$
$3 T_1-2 T_2=200\ldots\ldots (4)$
From second and third term
$2 T_1-3.5 T_2=-27\ldots\ldots (5)$
Solve equation (4) and (5), we get
$T_1=116^{\circ} C, T_2=74^{\circ} C$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "3 Marks Question" from PART - 2 CH - 10 Thermal Properties of Matter→PART - 2 CH - 10 Thermal Properties of Matter — all question types→Physics STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

According to the molecular kinetic theory of gases, what is the mean free path?

In Exercises $3.13$ and $3.14$, we have carefully distinguished between average speed and magnitude of average velocity. No such distinction is necessary when we consider instantaneous speed and magnitude of velocity. The instantaneous speed is always equal to the magnitude of instantaneous velocity. Why?

To simulate car accidents, auto manufacturers study the collisions of moving cars with mounted springs of different spring constants. Consider a typical simulation with a car of mass $1000 \ kg$ moving with a speed $18.0 \ km / h$ on a smooth road and colliding with a horizontally mounted spring of spring constant $5.25 \times 10^3 N m ^{-1}$. What is the maximum compression of the spring?

Calculate the specific heat capacity at constant volume for a gas. Given specific heat capacity at constant pressure is $6.85 \mathrm{cal} \mathrm{~mole}^{-1} \mathrm{~K}^{-2}, \mathrm{R}=8.31 \mathrm{~J} \mathrm{~mole}^{-1} \mathrm{~K}^{-1}$ and $\mathrm{J}=4.18 \mathrm{~J} \mathrm{cal}^{-1}$.

A thin prism is made of a material having refractive indices 1.61 and 1.65 for red and violet light. The dispersive power of the material is 0.07. It is found that a beam of yellow light passing through the prism suffers a minimum deviation of 4.0° in favourable conditions. Calculate the angle of the prism.

What are the different properties of the material used in heat thermometer?

Find the potential energy of a system of four particles placed at the vertices of a square of side $l$. Also obtain the potential at the centre of the square.

How much fraction of the K.E. of rolling is purely (i) translational (ii) rotational?

In an experiment, it was found that the string vibrates in $3$ loops when 'x' g was as mass of placed on the scale pan. What must be placed on the pan to make the string vibrate in 9 loops?

The reading of pressure meter attached to a closed pipe is $3.5 \times 10^5 Nm ^{-2}$. On opening the valve of the pipe, the reading of the pressure meter is reduced to $3.0 \times 10^5 Nm ^{-2}$. Calculate the speed of the water flowing in the pipe.