Two rods, A and B, of different materials having the same cross-sectional area are welded together as shown in the figure. Their thermal conductivities are $K_1$ and $K_2$. The thermal conductivity of the composite rod will be:

1. $\frac{K_1+K_2}{2}$
2. $\frac{3\left(K_1+K_2\right)}{2}$
3. $K_1+K_2$
4. $2\left(K_1+K_2\right)$

Two metal wires of identical dimensions are connected in series. If $\sigma$₁ and $\sigma$₂ are the conductivities of the metal wires respectively, the effective conductivity of the combination is

1. $\frac{{\displaystyle 2{\sigma }_1{\sigma }_2}}{{\displaystyle {\sigma }_1+{\sigma }_2}}$

2. $\frac{{\displaystyle {\sigma }_1{\sigma }_2}}{{\displaystyle 2{\sigma }_1{\sigma }_2}}$ 

3. $\frac{{\displaystyle {\sigma }_1+{\sigma }_2}}{{\displaystyle {\sigma }_1{\sigma }_2}}$  

4. $\frac{{\displaystyle {\sigma }_1{\sigma }_2}}{{\displaystyle {\sigma }_1+{\sigma }_2}}$

A slab of stone of area of 0.36 ${\mathrm{m}}^2$ and 

thickness 0.1 m is exposed on the lower 

surface to steam at $100°\mathrm{C}$. A block of ice 

at $0°\mathrm{C}$ rests on the upper surface of the slab.

In one hour 4.8 kg of ice is melted. The thermal

conductivity of slab is

(Given latent heat of fusion of ice 

=3.36x${10}^{5 }\mathrm{J} {\mathrm{kg}}^{-1}$)

(a) $1.24 \mathrm{J}/\mathrm{m}/\mathrm{s}/°\mathrm{C}$        (b) $1.29 \mathrm{J}/\mathrm{m}/\mathrm{s}/°\mathrm{C}$

(c) $2.05 \mathrm{J}/\mathrm{m}/\mathrm{s}/°\mathrm{C}$        (d) $1.02 \mathrm{J}/\mathrm{m}/\mathrm{s}/°\mathrm{C}$

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

Under steady state, the temperature of a body 

(1) Increases with time

(2) Decreases with time

(3) Does not change with time and is same at all the points of the body

(4) Does not change with time but is different at different points of the body