When 1 kg of ice at $0°\mathrm{C}$ melts to water at $0°\mathrm{C}$, the resulting change in its entropy, taking latent heat of ice to be $80 \mathrm{cal}/\mathrm{g},$ is

1.  $8\times {10}^4 \mathrm{cal}/\mathrm{K}$                                     

2.  $80 \mathrm{cal}/\mathrm{K}$

3.  $293 \mathrm{cal}/\mathrm{K}$                                         

4.  $273 \mathrm{cal}/\mathrm{K}$

A cylindrical metallic rod in thermal contact with two reservoirs of heat at its two ends conducts an amount of heat Q in time t. The metallic rod is melted and the material is formed into a rod of half the radius of the original rod. What is the amount of heat conducted by the new rod when placed in thermal contact with the two reserviors in time t ?

(1)Q/4                                         

(2)Q/16

(3)2Q                                           

(4)Q/2

On a new scale of temperature (which is linear) and called the W scale, the freezing and boiling points of water are $39°W$ and $239°W$ respectively. What will be the temperature on the new scale, corresponding to a temperature of $39°C$ on the Celsius scale?

1. $78°W$                                   

2. $117°W$

3. $200°W$                                 

4. $139°W$

The pressure applied from all directions on a cube is P. How much its temperature should be raised to maintain the original volume ? The volume elasticity of the cube is  $\beta$ and the coefficient of volume expansion is $\alpha$ -

1. $\frac{P}{\alpha \beta }$                                 

2. $\frac{P\alpha }{\beta }$

3. $\frac{P\beta }{\alpha }$                                 

4. $\frac{\alpha \beta }{P}$

The ratio of thermal conductivity of two rods of different material is 5 : 4. The two rods of same area of cross-section and same thermal resistance will have the lengths in the ratio 

(1) 4 : 5             

(2) 9 : 1

(3) 1 : 9             

(4) 5 : 4

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