Emissive and Absorptive Power

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

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

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. 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. Find the correct option among the following -
$[a\to$ absorptive power, $r\to$ reflective power, $t\to$ transmissive power $]$

1. $a+r+t=0$
2. $a+r+t=1$
3. $a+t=r$
4. $a+r=t$

Q. Two identical objects A and B are at temperatures $T_A$ and $T_B$ respectively, Both objects are placed in a room with perfectly absorbing walls maintained at a temperature $T(T_A>T>T_B)$. The objects A and B attain the temperature T eventually. Select the correct statements from the following.

1. A only emits radiation, while B only absorbs it until both attain the temperature T.
2. A loses more heat by radiation than it absorbs, while B absorbs more radiation than it emits, until they attain the temperature T.
3. Both A and B only absorb radiation, but do not emit it, until they attain the temperature T.
4. Each object continues to emit and absorb radiation even after attaining the temperature T.

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

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

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

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

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 in vacuum. Find the electric power needed to maintain the sheet at this temperature, given that its emissivity is $0.250$.
(Take $\sigma =5.67\times {10}^{-8}{\text{W/m}}^2-{\text{K}}^4$)

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

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