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

The coefficient of thermal conductivity depends upon

(1) Temperature difference of two surfaces

(2) Area of the plate

(3) Thickness of the plate

(4) Material of the plate

When two ends of a rod wrapped with cotton are maintained at different temperatures and, after some time, every point of the rod attains a constant temperature, then:

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

In variable state, the rate of flow of heat is controlled by
(1) Density of material               

(2) Specific heat

(3) Thermal conductivity             

(4) All the above factors

The dimensions of thermal resistance are
(1) ${\mathrm{M}}^{-1}{\mathrm{L}}^{-2}{\mathrm{T}}^3\mathrm{K}$           

(2) ${\mathrm{ML}}^2{\mathrm{T}}^{-2}{\mathrm{K}}^{-1}$

(3) ${\mathrm{ML}}^2{\mathrm{T}}^{-3}\mathrm{K}$               

(4) ${\mathrm{ML}}^2{\mathrm{T}}^{-2}{\mathrm{K}}^{-2}$