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

A solid copper cube of edges 1 cm is suspended in an evacuated enclosure. Its temperature is found to fall from 100$°\mathrm{C}$ to 99$°\mathrm{C}$ in 100 s . Another solid copper cube of edges 2 cm, with similar surface nature, is suspended in a similar manner. The time required for this cube to cool from 100$°\mathrm{C}$ to 99$°\mathrm{C}$ will be approximately -
(a) 25 s                  (b) 50 s  
(c) 200 s                 (d) 400 s

A body initially at 80$°\mathrm{C}$ cools to 64$°\mathrm{C}$ in 5 minutes and to 52$°\mathrm{C}$ in 10 minutes. The temperature of the body after 15 minutes will be 
(a) 42.7$°\mathrm{C}$                  (b) 35 $°\mathrm{C}$
(c) 47 $°\mathrm{C}$                    (d) 40 $°\mathrm{C}$

Four identical rods of same material are joined end to end to form a square. If the temperature difference between the ends of a diagonal is 100$°\mathrm{C}$, then the temperature difference between the ends of other diagonal will be -

(1) 0$°\mathrm{C}$ 

(2) $\frac{100}{\mathrm{l}}°\mathrm{C}$; where l is the length of each rod

(3) $\frac{100}{2\mathrm{l}}°\mathrm{C}$

(4) 100$°\mathrm{C}$

A cylindrical rod with one end in a steam chamber and the other end in ice results in melting of 0.1 gm of ice per second. If the rod is replaced by another with half the length and double the radius of the first and if the thermal conductivity of material of second rod is $\frac{1}{4}$ that of first, the rate at which ice melts in gm/sec will be -
(1) 3.2               

(2) 1.6

(3) 0.2               

(4) 0.1