Two identical conducting rods are first connected independently to two vessels, one containing water at 100$°\mathrm{C}$ and the other containing ice at 0$°\mathrm{C}$. In the second case, the rods are joined end to end and connected to the same vessels. Let ${\mathrm{q}}_1$ and ${\mathrm{q}}_2$ g / s be the rate of melting of ice in two cases respectively. The ratio of ${\mathrm{q}}_1$/${\mathrm{q}}_2$ is

(a) $\frac{1}{2}$                 (b) $\frac{2}{1}$
(c) $\frac{4}{1}$                 (d) $\frac{1}{4}$

A solid cube and a solid sphere of the same material have equal surface area. Both are at the same temperature 120$°\mathrm{C}$, then -

(1) Both the cube and the sphere cool down at the same rate

(2) The cube cools down faster than the sphere

(3) The sphere cools down faster than the cube

(4) Whichever is having more mass will cool down faster

Two bodies \(A\) and \(B\) have thermal emissivities of \(0.01\) and \(0.81\) respectively. The outer surface areas of the two bodies are the same. The two bodies emit total radiant power at the same rate. The wavelength \(\lambda_B\) corresponding to maximum spectral radiancy in the radiation from \(B\) is shifted from the wavelength corresponding to maximum spectral radiancy in the radiation from \(A\), by \(1.00~\mu\text{m}\). If the temperature of \(A\) is \(5802~\text{K}\):

A black body is at a temperature of 2880 K. The energy of radiation emitted by this object with wavelength between 499 nm and 500 nm is ${\mathrm{U}}_1$, between 999 nm and 1000nm is ${\mathrm{U}}_2$ and between 1499 nm and 1500 nm is ${\mathrm{U}}_3$. [Given : Wein's constant $\mathrm{b}=2.88\times {10}^6 \mathrm{nm} \mathrm{K}$}.  Then

(1) ${\mathrm{U}}_1=0$          

(2) ${\mathrm{U}}_3=0$

(3) ${\mathrm{U}}_1>{\mathrm{U}}_2$        

(4) ${\mathrm{U}}_2>{\mathrm{U}}_1$

A black metal foil is warmed by radiation from a small sphere at temperature T and at a distance d where surrounding temperature is $T_o$. It is found that the power received by the foil is P. If both the temperature and the distance are doubled, the power received by the foil will be - [Assume $T>>T_o$]
1. 16P                 

2.  4P

3. 2P                   

4. P

Three rods of same dimensions are arranged as shown in figure they have thermal conductivities ${\mathrm{K}}_1, {\mathrm{K}}_2$ and ${\mathrm{K}}_3$ The points P and Q are maintained at different temperatures for the heat to flow at the same rate along PRQ and PQ then which of the following option is correct ?

 
(1) ${\mathrm{K}}_3=\frac{1}{2}\left({\mathrm{K}}_1+{\mathrm{K}}_2\right)$

(2) ${\mathrm{K}}_3={\mathrm{K}}_1+{\mathrm{K}}_2$

(3) ${\mathrm{K}}_3=\frac{{\mathrm{K}}_1{\mathrm{K}}_2}{{\mathrm{K}}_1+{\mathrm{K}}_2}$

(4) ${\mathrm{K}}_3=2\left({\mathrm{K}}_1+{\mathrm{K}}_2\right)$

Two metallic spheres ${\mathrm{S}}_1$ and ${\mathrm{S}}_2$ are made of the same material and have identical surface finish. The mass of ${\mathrm{S}}_1$ is three times that of ${\mathrm{S}}_2$. Both the spheres are heated to the same high temperature and placed in the same room having lower temperature but are thermally insulated from each other. The ratio of the initial rate of cooling of ${\mathrm{S}}_1$ to that of ${\mathrm{S}}_2$ is 
(1) $1/3$             

(2) ${\left(1/3\right)}^{1/3}$

(3) $1/\sqrt{3}$          

(4) $\sqrt{3}/1$

Three discs \(A,B\) and \(C\) having radii \(2~\text{m},4~\text{m},\) and \(6~\text{m}\) respectively are coated with carbon black on their surfaces. The wavelengths corresponding to maximum intensity are \(300~\text{nm},400~\text{nm},\) and \(500~\text{nm}\) respectively. The power radiated by them are \(Q_a,Q_b,\) and \(Q_c\) respectively, then:
1. \(Q_a\) is maximum
2. \(Q_b\) is maximum
3. \(Q_c\) is maximum
4. \(Q_a=Q_b=Q_c\)

The total energy radiated from a black body source is collected for one minute and is used to heat a quantity of water. The temperature of water is found to increase  from   20$°\mathrm{C}$ to 20.5$°\mathrm{C}$ . If the absolute temperature of the black body is doubled and the experiment is repeated with the same quantity of water at 20$°\mathrm{C}$, the temperature of water will be 

1. 21$°\mathrm{C}$               2. 22$°\mathrm{C}$ 
3. 24$°\mathrm{C}$               4. 28$°\mathrm{C}$ 

A solid sphere and a hollow sphere of the same material and size are heated to the same temperature and allowed to cool in the same surroundings. If the temperature difference between each sphere and its surroundings is same , then

(1) The hollow sphere will cool at a faster rate for all values of T

(2) The solid sphere will cool at a faster rate for all values of T

(3) Both spheres will cool at the same rate for all values of T

(4) Both spheres will cool at the same rate only for small values of T