The energy distribution E with the wavelength $\left(\mathrm{\lambda }\right)$ for the black body radiation at temperature T Kelvin is shown in the figure. As the temperature is increased the maxima will:
     

1.	Shift towards left and become higher
2.	Rise high but will not shift
3.	Shift towards right and become higher
4.	Shift towards left and the curve will become broader

Which of the following graphs correctly represents the relation between \(ln~E\) and \(ln~T\) where \(E\) is the amount of radiation emitted per unit time from a unit area of a body and \(T\) is the absolute temperature?\(\left (Take~\sigma =5.67\times 10^{-8} ~W~m^{-2}~K^{-4}~and~0<\epsilon <1 \right )\)

1.		2.
3.		4.	Both 1 and 3

A block of metal is heated to a temperature much higher than the room temperature and allowed to cool in a room free from air currents. Which of the following curves correctly represents the rate of cooling?

1.		2.
3.		4.

One end of a copper rod of uniform cross-section and of length 3.1 m is kept in contact with ice, and the other end with water at \(100^{\circ}\mathrm{C}\). At what point along its length should a temperature of \(200^{\circ}\mathrm{C}\) be maintained so that in steady-state, the mass of ice melting be equal to that of the steam produced in the same interval time? (Assume that the whole system is insulated from the surroundings. Latent heat of fusion of ice and vaporisation of water are 80 cal/gm and 540 cal/gm respectively)
     

Three rods of identical area of cross-section and made from the same metal form the sides of an isosceles triangle ABC, which is right-angled at B. The points A and B are maintained at temperatures T and $\sqrt{2}\mathrm{T}$ respectively. In the steady state, the temperature of point C is ${\mathrm{T}}_{\mathrm{C}}$. Assuming that only heat conduction takes place, $\frac{{\mathrm{T}}_{\mathrm{C}}}{\mathrm{T}}$ is equal to:
1. $\frac{1}{\left(\sqrt{2}+1\right)}$
2. $\frac{3}{\left(\sqrt{2}+1\right)}$
3. $\frac{1}{2\left(\sqrt{2}-1\right)}$                  
4. $\frac{1}{\sqrt{3}\left(\sqrt{2}-1\right)}$

Consider two hot bodies, ${\mathrm{B}}_1$ and ${\mathrm{B}}_2$ which have temperatures of \(100^{\circ}\mathrm{C}\)$\mathrm{}$ and \(80^{\circ}\mathrm{C}\)$\mathrm{}$ respectively at t=0. The temperature of the surroundings is \(40^{\circ}\mathrm{C}\)$\mathrm{}$. The ratio of the respective rates of cooling ${\mathrm{R}}_1$ and ${\mathrm{R}}_2$ of these two bodies at t = 0 will be:
1. ${\mathrm{R}}_1:{\mathrm{R}}_2=3:2$
2. ${\mathrm{R}}_1:{\mathrm{R}}_2=5:4$
3. ${\mathrm{R}}_1:{\mathrm{R}}_2=2:3$
4. ${\mathrm{R}}_1:{\mathrm{R}}_2=4:5$

If the sun’s surface radiates heat at $6.3\times {10}^7$ ${\mathrm{Wm}}^{-\mathrm{2 }}$then the temperature of the sun, assuming it to be a black body, will be:
$\left(\mathrm{\sigma }=5.7\times {10}^{-8}\right)$ ${\mathrm{Wm}}^{-2}{\mathrm{K}}^{-4}$
1. $5.8\times {10}^3$ $\mathrm{K}$
2. $8.5\times {10}^3$ $\mathrm{K}$
3. $3.5\times {10}^8$ $\mathrm{K}$
4. $5.3\times {10}^8$ $\mathrm{K}$

If the temperature of the body is increased from \(-73^{\circ}\mathrm{C}\)$\mathrm{}$ to \(327^{\circ}\mathrm{C}\)$\mathrm{}$, then the ratio of energy emitted per second in both cases is:
1. 1 : 3                         
2. 1 : 81
3. 1 : 27                       
4. 1 : 9

The temperature of an object is \(400^{\circ}\mathrm{C}\)$\mathrm{}$. The temperature of the surroundings may be assumed to be negligible. What temperature would cause the energy to radiate twice as quickly? (Given, \(2^{\frac{1}{4}} \approx 1.18\))
1. \(200^{\circ}\mathrm{C}\)
2. 200 K
3. \(800^{\circ}\mathrm{C}\)$\mathrm{}$         
4. 800 K

A black body has a maximum wavelength at a temperature of 2000 K. Its corresponding wavelength at temperatures of 3000 K will be: