Q. A hollow and a solid sphere of same material and identical outer surface under identical condition are heated to the same temperature at the same time (both have same $e, a$) :

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A

In the beginning both will emit equal amount of radiation per unit time

B

In the beginning both will absorb equal amount of radiation per unit time

C

Both spheres will have same rate of fall of temperature (dT/dt)

D

Both spheres will have equal temperatures at any moment

Solution:

As initially they are at same temperature their radiation rates will be equal and their absorption rate from surrounding will also be equal but as time passes, due to the difference in masses of the two their temperature will differ and rates will also be changed at later instants and due to this rate of fall of temperatures will also be different at later instants.

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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. A hollow and a solid sphere of same material and identical outer surface under identical condition are heated to the same temperature at the same time (both have same $e, a$) :

In the beginning both will emit equal amount of radiation per unit time

In the beginning both will absorb equal amount of radiation per unit time

Both spheres will have same rate of fall of temperature (dT/dt)

Both spheres will have equal temperatures at any moment

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