The coefficients of thermal conductivity of copper, mercury and glass are respectively ${\mathrm{K}}_{\mathrm{c}}$, ${\mathrm{K}}_{\mathrm{m}}$ and ${\mathrm{K}}_{\mathrm{g}}$ such that ${\mathrm{K}}_{\mathrm{c}}>{\mathrm{K}}_{\mathrm{m}}>{\mathrm{K}}_{\mathrm{g}}$. If the same quantity of heat is to flow per second per unit area of each and corresponding temperature gradients are ${\mathrm{X}}_{\mathrm{c}}$, ${\mathrm{X}}_{\mathrm{m}}$ and ${\mathrm{X}}_{\mathrm{g}}$, then 
(1) ${\mathrm{X}}_{\mathrm{c}}={\mathrm{X}}_{\mathrm{m}}={\mathrm{X}}_{\mathrm{g}}$                 

(2) ${\mathrm{X}}_{\mathrm{c}}>{\mathrm{X}}_{\mathrm{m}}>{\mathrm{X}}_{\mathrm{g}}$

(3) ${\mathrm{X}}_{\mathrm{c}}<{\mathrm{X}}_{\mathrm{m}}<{\mathrm{X}}_{\mathrm{g}}$                 

(4) ${\mathrm{X}}_{\mathrm{m}}<{\mathrm{X}}_{\mathrm{c}}<{\mathrm{X}}_{\mathrm{g}}$

Two spheres of different materials one with double the radius and one-fourth wall thickness of the other, are filled with ice. If the time taken for complete melting of ice in the larger sphere is 25 minutes and that for smaller sphere 16 minutes, the ratio of thermal conductivities of the materials of larger sphere to the smaller sphere is 
(1) 4 : 5                   

(2) 5 : 4

(3) 25 : 1                 

(4) 8 : 25

Consider a compound slab consisting of two different materials having an equal thickness and thermal conductivities K and 2K respectively. The equivalent thermal conductivity of the slab if the materials are joined by ends is:
(a) $\sqrt{2\mathrm{K}}$                  (b) 3K
(c) $\frac{4}{3}\mathrm{K}$                    (d) $\frac{2}{3}\mathrm{K}$

A wall has two layers A and B made of different materials. The thickness of both the layers is the same. The thermal conductivity of A and B are ${\mathrm{K}}_{\mathrm{A}}$ and ${\mathrm{K}}_{\mathrm{B}}$ such that  ${\mathrm{K}}_{\mathrm{A}}$ = 3${\mathrm{K}}_{\mathrm{B}}$. The temperature across the wall is 20°C. In thermal equilibrium 

(1) The temperature difference across A = 15°C

(2) The temperature difference across A = 5°C

(3) The temperature difference across A is 10°C

(4) The rate of transfer of heat through A is more than that through B.

Which of the following circular rods (given radius r and length l) each made of the same material as whose ends are maintained at the same temperature will conduct most heat ?

(1) $\mathrm{r}=2{\mathrm{r}}_0 ; \mathrm{l}=2{\mathrm{l}}_0$           

(2) $\mathrm{r}=2{\mathrm{r}}_0 ; \mathrm{l}={\mathrm{l}}_0$

(3) $\mathrm{r}={\mathrm{r}}_0 ; \mathrm{l}={\mathrm{l}}_0$               

(4) $\mathrm{r}={\mathrm{r}}_0 ; \mathrm{l}=2{\mathrm{l}}_0$

When fluids are heated from the bottom, convection currents are produced because -

(1) Molecular motion of fluid becomes aligned

(2) Molecular collisions take place within the fluid

(3) Heated fluid becomes more dense than the cold fluid above it

(4) Heated fluid becomes less dense than the cold fluid above it

When p calories of heat is given to a body, it absorbs q calories; then the absorbtion power of body will be ?
(1) p/q                         

(2) q/p

(3) ${\mathrm{p}}^2/{\mathrm{q}}^2$                     

(4) ${\mathrm{q}}^2/{\mathrm{p}}^2$

On investigation of light from three different stars A, B and C, it was found that in the spectrum of A the intensity of red colour is maximum, in B the intensity of blue colour is maximum and in C the intensity of yellow colour is maximum. From these observations it can be concluded that

(1) The temperature of A is maximum, B is minimum and C is intermediate

(2) The temperature of A is maximum, C is minimum and B is intermediate

(3) The temperature of B is maximum, A is minimum and C is intermediate

(4) The temperature of C is maximum, B is minimum and A is intermediate

A black body at a temperature of 227$°\mathrm{C}$ radiates heat energy at the rate of 5 $\mathrm{cal}/{\mathrm{cm}}^2-\sec$. At a temperature of $727°\mathrm{C}$, the rate of heat radiated per unit area in $\mathrm{cal}/{\mathrm{cm}}^2$ will be 
(1) 80                     

(2) 160

(3) 250                   

(4) 500

The area of a hole of heat furnace is ${10}^{-4} {\mathrm{m}}^2$. It radiates $1.58\times {10}^5$ calories of heat per hour. If the emissivity of the furnace is 0.80, then its temperature is
(1) 1500 K           

(2) 2000 K

(3) 2500 K           

(4) 3000 K