Kirchoff's Law

Q. A black body has wavelength corresponding to the maximum energy equals to ${\lambda }_m$ at $2000\text{K}$. Its corresponding wavelength at $3000\text{K}$ will be :

1. $\frac{3}{2}{\lambda }_m$
2. $\frac{2}{3}{\lambda }_m$
3. $\frac{16}{81}{\lambda }_m$
4. $\frac{81}{16}{\lambda }_m$

Q. Which of the following graphs correctly represents the variation of $\log {\lambda }_m$ with $\log T$?
[${\lambda }_m$ is the wavelength corresponding to maximum intensity of radiation and $T$ represents absolute temperature.]

1. 
2. 
3. 
4. 

Q. The plots for intensity versus wavelength for three black bodies at temperatures $T_1,T_2,T_3$ respectively are shown in figure. Their temperatures are such that

1. $T_1>T_2>T_3$
2. $T_1>T_3>T_2$
3. $T_2>T_3>T_1$
4. $T_3>T_2>T_1$

Q. The emissive power of a black body at $T=300\text{K}$ is $100{\text{W/m}}^2$. Consider a body $B$ of area $A=10{\text{m}}^2$, coefficient of reflectivity $r=0.3$ and coefficient of transmission $t=0.5$. Its temperature is $300\text{K}$. Then choose the correct statement.

1. The emissive power of $B$ is $20{\text{W/m}}^2$.
2. The emissive power of $B$ is $200{\text{W/m}}^2$.
3. The power emitted by $B$ is $100\text{W}$.
4. The emissivity of $B$ is $0.2$.

Q. A black body is at rest at a temperature of $2880\text{K}$. The energy of radiation emitted by this object with wavelength between $499\text{n-m}$ and $500\text{n-m}$ is $U_1$, between $999$ and $1000\text{nm}$ is $U_2$ and between $1499\text{nm}$ and $1500\text{nm}$ is $U_3$. The Wien's constant $b=2.88\times {10}^6\text{nm-K}$. Then

1. $U_1=0$
2. $U_3=0$
3. $U_1>U_2$
4. $U_2>U_1$

Q.

Experimental investigations show that the intensity of the solar radiation is maximum for a wavelength $4750\hat{A}$ in the visible region. If the surface temperature of the sun is 6000 K, what is the value of the Wien’s constant b?

1. $2.85mK$

2. $0.285mK$

3. $2.85\times {10}^{-2}mK$

4. $2.85\times {10}^{-3}mK$

Q.

Which one of the following statements is not true about thermal radiations?

1. All bodies emit thermal radiations at all temperatures

2. Thermal radiations are electromagnetic waves

3. Thermal radiations are not reflected from a mirror

4. Thermal radiations travel in free space with a velocity of $3\times {10}^{8}m{s}^{-1}$