Q. A composite slab consists of two parts of equal thickness. The thermal conductivity of one is twice that of the other. What will be the ratio of temperature difference across the two layers in the state of equilibrium ?

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A

1

10%

B

2

65%

C

3

13%

D

4

12%

Solution:

We use
$\frac{k_{1} A\left(\Delta T_{1}\right)}{l} =\frac{k_{2} A\left(\Delta T_{2}\right)}{l}$
$\frac{\Delta T_{1}}{\Delta T_{2}} =\frac{k_{2}}{k_{1}}$
$=\frac{2 k_{1}}{k_{1}}=2$

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2. A wall is made of equally thick layers $A$ and $B$ of different materials. Thermal conductivity of $A$ is twice that of $B$. In the steady state, the temperature difference across the wall is $36^{\circ}C$. The temperature difference across the layer $A$ is

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Q. A composite slab consists of two parts of equal thickness. The thermal conductivity of one is twice that of the other. What will be the ratio of temperature difference across the two layers in the state of equilibrium ?

1

2

3

4

We use $\frac{k_{1} A\left(\Delta T_{1}\right)}{l} =\frac{k_{2} A\left(\Delta T_{2}\right)}{l}$ $\frac{\Delta T_{1}}{\Delta T_{2}} =\frac{k_{2}}{k_{1}}$ $=\frac{2 k_{1}}{k_{1}}=2$

Questions from Thermal Properties of Matter

1. If the temperature difference on the two sides of a wall increases from $ 100{}^\circ C $ to $ 200{}^\circ C $ , its thermal conductivity

2. A wall is made of equally thick layers $A$ and $B$ of different materials. Thermal conductivity of $A$ is twice that of $B$. In the steady state, the temperature difference across the wall is $36^{\circ}C$. The temperature difference across the layer $A$ is

3. The radiation emitted by a star $A$ is $10,000$ times that of the sun. If the surface temperatures of the sun and the star $A$ are $8000 \, K$ and $2000 \, K$ respectively. The ratio of the radii of the star $A$ and the sun is

4. A black body at $1373$ $℃$ emits maximum energy corresponding to a wavelength of $1.78$ microns. The temperature of the moon for which $\lambda _{m}=14$ micron would be

Physics Most Viewed Questions

1. If $E$ and $G$ respectively denote energy and gravitational constant, then $\frac{ E }{ G }$ has the dimensions of:

2. The de Broglie wavelength of an electron moving with kinetic energy of $144 \,eV$ is nearly

3. A car starts from rest and accelerates at $5\, m / s ^{2}$ At $t=4\, s$, a ball is dropped out of a window by a person sitting in the car. What is the velocity and acceleration of the ball at $t =6\, s$ ? (Take $\left. g =10\, m / s ^{2}\right)$

4. A wheel with $20$ metallic spokes each $1\, m$ long is rotated with a speed of $120\, rpm$ in a plane perpendicular to a magnetic field of $0.4\, G$. The induced emf between the axle and rim of the wheel will be, $(1 G = 10^{-4}\, T)$

5. A barometer is constructed using a liquid (density $= 760 \,kg/m^{3})$ What would be the height of the liquid column, when a mercury barometer reads $76\, cm$ ? (density of mercury $= 13600 kg/m^{3})$

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We use
$\frac{k_{1} A\left(\Delta T_{1}\right)}{l} =\frac{k_{2} A\left(\Delta T_{2}\right)}{l}$
$\frac{\Delta T_{1}}{\Delta T_{2}} =\frac{k_{2}}{k_{1}}$
$=\frac{2 k_{1}}{k_{1}}=2$

5. A barometer is constructed using a liquid (density $= 760 \,kg/m^{3})$ What would be the height of the liquid column, when a mercury barometer reads $76\, cm$ ?
(density of mercury $= 13600 kg/m^{3})$