Q. The plots of intensity vs wavelength for two black bodies at temperature $T_{1}$ and $T_{2}$ such that $T_{2}=2 T_{1}$ respectively are as shown. Let the energy radiated per second by body $1$ and body $2$ be $E_{1}$ and $E_{2}$ respectively. Pick up the correct statement(s).

Thermal Properties of Matter Report Error

A

$E_{1}=16\, E_{2}$

B

$E_{1}$ may be equal to $16$ times of $E_{2}$

C

The area under curve $1$ and area under curve $2$ will be same

D

Area under curve $2$ is larger than area under curve $1$

Solution:

As in the situation surface area of the bodies is not specified we cannot comment on total energy radiated by the bodies which is given by the are a under the spectral intensity curves. If the areas of the two bodies are equal then option (B) can be correct

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

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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

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

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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

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5. Three rods made from the same material and having the same cross-sectional area, form the sides of an isosceles triangle $ABC$ , right-angled at $B$ . The points $A$ and $B$ are maintained at temperature $T$ and $\sqrt{2}T$ , respectively. In steady-state, the temperature of the point $C$ is $T_{C}$ . Assuming that only heat conduction takes place along the lengths of the rods, the value of $\frac{T_{C}}{T}$ is

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

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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 $\left. g =10\, m / s ^{2}\right)$

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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, $(1 G = 10^{-4}\, T)$

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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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Q. The plots of intensity vs wavelength for two black bodies at temperature $T_{1}$ and $T_{2}$ such that $T_{2}=2 T_{1}$ respectively are as shown. Let the energy radiated per second by body $1$ and body $2$ be $E_{1}$ and $E_{2}$ respectively. Pick up the correct statement(s).

$E_{1}=16\, E_{2}$

$E_{1}$ may be equal to $16$ times of $E_{2}$

The area under curve $1$ and area under curve $2$ will be same

Area under curve $2$ is larger than area under curve $1$

As in the situation surface area of the bodies is not specified we cannot comment on total energy radiated by the bodies which is given by the are a under the spectral intensity curves. If the areas of the two bodies are equal then option (B) can be correct

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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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 $= 13600 kg/m^{3})$