Emissive and Absorptive Power

Q. A heated body emits radiation which has maximum intensity at frequency $v_m$. If the temperature of the body is doubled:

1. the maximum intensity radiation will be at frequency $2v_m$
2. the maximum intensity radiation will be at frequency $\frac{1}{2}{v}_m$
3. the total emitted energy will increase by a factor 16
4. the total emitted energy will increase by a factor 2

Q. Application of convection, radiation, conduction

Q. Rate of emission of a black body at ${546}^{\circ }C$ is $E$. Then the rate of emission of radiation of body at $0^{\circ }C$ will be

1. $81E$
2. $3E$
3. $\frac{E}{3}$
4. $\frac{E}{81}$

Q. A copper sphere is suspended in an evacuated chamber maintained at $300\text{K}$. The sphere is maintained at a constant temperature of $500\text{K}$ by heating it electrically. A total of $300\text{W}$ of electric power is needed to do it. When half of the surface of the copper sphere is completely blackened, $600\text{W}$ is needed to maintain the same temperature of the sphere. Calculate the emissivity(e) of copper.

Q.

The rate of radiation of a black body at $0^{o}C$ is E J/sec. The rate of radiation of this black body at ${273}^{o}C$ will be

1. 

2. 

3. 

4. 

Q. Discuss briefly energy distribution of black body radiation

Q.

A point source of heat of power $\mathrm{P}$ is placed at the center of a spherical shell of mean radius $\mathrm{R}$. The material of the shell has thermal conductivity $\mathrm{k}$. If the temperature difference between the outer and the inner surface of the shell is not to exceed $\mathrm{T}$., then the thickness of the shell should not be less than

1. $\frac{2{\mathrm{\pi R}}^2\mathrm{kT}}{\mathrm{P}}$

2. $\frac{4{\mathrm{\pi R}}^2\mathrm{kT}}{\mathrm{P}}$

3. $\frac{{\mathrm{\pi R}}^2\mathrm{kT}}{\mathrm{P}}$

4. $\frac{{\mathrm{\pi R}}^2\mathrm{kT}}{4\mathrm{P}}$

Q. The plots of intensity versus wavelength for three black bodies at temperatures $T_1,T_{2}and{T}_3$ respectively are as shown. Their temperature are such that

1. 
2. 
3. 
4. 

Q. The operating temperature of a tungsten filament in an incandescent lamp is $2000\text{K}$ and its emissivity is $0.3$. Find the surface area of the filament of a $25\text{watt}$ lamp.
Stefen's constant $\sigma =5.67\times {10}^{-8}{\text{W m}}^{-2}{\text{K}}^{-4}$

1. $0.412\times {10}^{-5}{\text{m}}^2$
2. $0.918\times {10}^{-4}{\text{m}}^2$
3. $0.212\times {10}^{-4}{\text{m}}^2$
4. $0.416\times {10}^{-4}{\text{m}}^2$

Q. When the temperature of a black body increases, it is observed that the wavelength corresponding to maximum energy changes from $0.26\mu \text{m}$ to $0.13\mu \text{m}$ Then ratio of the emissive power of the body at respective temperature is

1. $4/1$
2. $1/4$
3. $16/1$
4. $1/16$

Q.

Ice at –20° C is added to 50 g of water at 40°C. When the temperature of the mixture reaches 0°C, it is found that 20 g of ice is still not melted. The amount of ice added to the water was close to

(Specific heat of water = 4.2 J/g/°C)

Specific heat of Ice = 2.1 J/g/°C

The heat of fusion of water at 0°C = 334 J/g)

1. 50 g

2. 40 g

3. 60 g

4. 100 g

Q. The graph shown in the adjacent diagram represents the variation of temperature $\left(T\right)$ of two bodies, $x$ and $y$ having same surface area, with time $\left(t\right)$ due to the emission of radiation. Find the correct relation between the emissivity $\left(e\right)$ and absorptivity $\left(a\right)$ of the two bodies.

1. $e_x>e_y$ and $a_x<a_y$
2. $e_x<e_y$ and $a_x>a_y$
3. $e_x>e_y$ and $a_x>a_y$
4. $e_x<e_y$ and $a_x<a_y$

Q.

The temperature of 170g of water at ${50}^{o}C$ is lowered to $5^{o}C$ by adding certain amount of ice to it. Find the mass of the ice added.

(Given: Specific heat capacity of water$=4200JK{g}^{-1}{}^{o}C^{-1}$ and specific latent heat of ice$=33600JK{g}^{-1}$)

Q. Radiation coming from transitions $n=2$ to $n=1$ of hydrogen atoms fall on $H{e}^{+}$ ions in $n=1$ and $n=2$ states. The possible transition of helium ions as they absorb energy from the radiation is

1. $n=1\to n=4$
2. $n=2\to n=4$
3. $n=2\to n=5$
4. $n=2\to n=3$

Q.

If wavelengths of maximum intensity of radiations emitted by the sun and the moon are $0.5\times {10}^{-5}mand{10}^{-4}m$ respectively, the ratio of their temperatures is

1. 1/100

2. 1/200

3. 100

4. 200

Q. The four surfaces used in the Leslie's cube experiment of a cube are kept

1. at different temperatures
2. at same temperature
3. two surfaces at same temperature and two at different temperature
4. three surfaces at same temperature and one at different temperature

Q. The operating temperature of an incandescent bulb (with a tungsten filament) of power $60\text{W}$ is $3000\text{K}$. If the surface area of the filament be $25{\text{mm}}^2$. Find its emissivity $e$.$(\sigma =5.67\times {10}^{-8}\text{W}/{\text{m}}^2-{\text{K}}^4)$

1. $0.52$
2. $0.48$
3. $0.64$
4. $0.36$

Q. 37.a source of power 600 kilowatt emits Photon which incident on a surface 2.5 M away out of which 50% is reflect back, what is radiation pressure on surface

Q.

The rate of radiation of a black body at $0^0$ C is EJ/sec. The rate of radiation of this black body at ${273}^0$ C will be

1. 16 E

2. E

3. 8 E

4. 4 E

Q. A thin brass rectangular sheet of sides $15.0\text{cm}$ and $12.0\text{cm}$ is heated in a furnace to ${527}^{\circ }\text{C}$ and taken out. Find the electric power needed to maintain the sheet at this temperature, given that its emissivity is $0.250$ (Neglect heat loss due to convection and $\sigma =5.67\times {10}^{-8}{\text{W/m}}^2-{\text{K}}^4$)

1. $300\text{W}$
2. $209\text{W}$
3. $250\text{W}$
4. $400\text{W}$

Q. Two parallel long smooth conducting rails seperated by a distance $l$ are connected by a movable conducting connector of mass ${}^{\prime }{m}^{\prime }$. Terminals of the rails are connected by the resistor $R$ and the capacitor $C$ as shown. A uniform magnetic field $B$ perpendicular to the plane of the rails is switched on. The connector is dragged by a constant force $F$. If the force $F$ is applied at $t=0$, then find the terminal velocity of the connector (in $m/s$. Given that $FR=4B^2{l}^2.$

Q. A water heater raises temperature of $1\text{kg}$ of water by $30{}^{\circ }\text{C}$ in $10\text{min}$. How long will it take the same heater to raise $3\text{kg}$ of oil through the same temperature. Given that specific heat of water is twice of oil.

1. $15\text{min}$
2. $5\text{min}$
3. $30\text{min}$
4. $60\text{min}$

Q. Between two wavelengths $500A^{\circ }$ and $1000A^{\circ },a_{\lambda }$ is the absorptive power and $e_{\lambda }$ is the emissive power of a body. If $E_{\lambda }$ is the emissive power of a perfectly black body then according to Kirchhoff's law,

1. $e_{\lambda }=a_{\lambda }=E_{\lambda }$
2. $e_{\lambda }=a_{\lambda }{E}_{\lambda }$
3. $e_{\lambda }{a}_{\lambda }{E}_{\lambda }=\text{constant}$
4. $\frac{a_{\lambda }}{e_{\lambda }}=\frac{1}{2}{E}_{\lambda }$

Q. A spherical body having radius $r$ is radiating energy $Q$ at a given temperature. If its radius is doubled then for same time, energy radiated will be

1. $\frac{1}{2}Q$
2. $\frac{1}{4}Q$
3. $2Q$
4. $4Q$

Q. A spherical body radiates $300\text{W}$ power at $650\text{K}$. If the radius were halved and temperature doubled, then find the power radiated.

1. $600\text{W}$
2. $300\text{W}$
3. $900\text{W}$
4. $1200\text{W}$

Q. Figure shows the net power dissipated in $R$ versus the current in a simple circuit shown.

1. The internal resistance of battery is $0.2\Omega$.
2. The emf of battery is $2\text{V}$
3. $R$ at which power is $5\text{W}$ is $2.5\Omega$
4. At $i$ = $2\text{A}$, power is $3.2\text{W}$

Q.

Two spheres P and Q, of same colour having radii 8 cm and 2 cm are maintained at temperatures ${127}^{o}C$ and ${527}^{o}C$ respectively. The ratio of energy radiated by P and Q is

1. 0.054

2. 0.0034

3. 1

4. 2

Q.

If $K$ denotes coefficient of thermal conductivity, $d$ the density and $C$ the specific heat, the unit of $X$, where $X=\frac{K}{dC}$ will be,

1. $cm{s}^{-1}$

2. $c{m}^2{s}^{-2}$

3. $cms$

4. $c{m}^2{s}^{-1}$

Q. The spectral emissive power $E_{\lambda }$ for a black body at temperature $T_1$ is plotted against the wavelength and area under the curve is found to be $A$. At a different temperature $T_2$, the area is found to be $9A$. Than ${\lambda }_1/{\lambda }_2$

1. $3$
2. $1/\sqrt{3}$
3. $1/3$
4. $\sqrt{3}$

Q. A spherical body of area $300{\text{cm}}^2$ has emissive power of $3000{\text{J/m}}^2\text{s}$. Find the amount of thermal energy radiated by the body in $10\text{s}$.

1. $5000\text{J}$
2. $1000\text{J}$
3. $9000\text{J}$
4. $900\text{J}$