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

One end of a copper rod of length 1.0 m and area of cross-section ${10}^{-3} {\mathrm{m}}^2$ is immersed in boiling water and the other end in ice. If the coefficient of thermal conductivity of copper is 92 cal/m-s $°\mathrm{C}$ and the latent heat of ice is $8\times {10}^4$ cal/kg, then the amount of ice which will melt in one minute is -

(a) $9.2\times {10}^{-3}$ kg         (b) $8\times {10}^{-3}$
(c) $6.9\times {10}^{-3}$              (d) $5.4\times {10}^{-3}$

An ice box used for keeping eatable cold has a total wall area of 1 ${\mathrm{metre}}^2$ and a wall thickness of 5.0 cm. The thermal conductivity of the ice box is K = 0.01 joule/metre-s-$°\mathrm{C}$. It is filled with ice at 0$°\mathrm{C}$ along with eatables on a day when the temperature is 30°C. The latent heat of fusion of ice is $334 \times {10}^3 joules/kg$. The amount of ice melted in one day is ( 1 day = 86,400 seconds ) 
(a) 776 gms            (b) 7760 gms  
(c) 11520 gms         (d) 1552 gms

Five rods of the same dimensions are arranged as shown in the figure. They have thermal conductivities ${\mathrm{K}}_1, {\mathrm{K}}_2, {\mathrm{K}}_3, {\mathrm{K}}_4$ and ${\mathrm{K}}_5$. When points A and B are maintained at different temperatures, no heat flows through the central rod if :

(1) ${\mathrm{K}}_1={\mathrm{K}}_4$ and ${\mathrm{K}}_2={\mathrm{K}}_3$

(2) ${\mathrm{K}}_1{\mathrm{K}}_4={\mathrm{K}}_2{\mathrm{K}}_3$

(3) ${\mathrm{K}}_1{\mathrm{K}}_2={\mathrm{K}}_3{\mathrm{K}}_4$

(4) $\frac{{\mathrm{K}}_1}{{\mathrm{K}}_4}=\frac{{\mathrm{K}}_2}{{\mathrm{K}}_3}$

A hot metallic sphere of radius r radiates heat. It's rate of cooling is
(1) Independent of r             

(2) Proportional to r

(3) Proportional to ${\mathrm{r}}^2$             

(4) Proportional to 1/r

A solid copper sphere (density $\mathrm{\rho }$ and specific heat capacity c) of radius r at an initial temperature 200K is suspended inside a chamber whose walls are at almost 0K. The time required (in $\mathrm{\mu }$s) for the temperature of the sphere to drop to 100 K is 
(1) $\frac{72}{7}\frac{\mathrm{r\rho c}}{\mathrm{\sigma }}$                  

(2) $\frac{7}{72}\frac{\mathrm{r\rho c}}{\mathrm{\sigma }}$

(3) $\frac{27}{7}\frac{\mathrm{r\rho c}}{\mathrm{\sigma }}$                 

(4) $\frac{7}{27}\frac{\mathrm{r\rho c}}{\mathrm{\sigma }}$