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

Two walls of thicknesses ${\mathrm{d}}_1$ and ${\mathrm{d}}_2$ and thermal conductivities ${\mathrm{k}}_1$ and ${\mathrm{k}}_2$ are in contact. In the steady state, if the temperatures at the outer surfaces  are ${\mathrm{T}}_1$ and ${\mathrm{T}}_2$, the temperature at the common wall is  -

(1) $\frac{{\mathrm{k}}_1{\mathrm{T}}_1{\mathrm{d}}_2+{\mathrm{k}}_2{\mathrm{T}}_2{\mathrm{d}}_1}{{\mathrm{k}}_1{\mathrm{d}}_2+{\mathrm{k}}_2{\mathrm{d}}_1}$                     

(2)$\frac{{\mathrm{k}}_1{\mathrm{T}}_1+{\mathrm{k}}_2{\mathrm{d}}_2}{{\mathrm{d}}_1+{\mathrm{d}}_2}$

(3) $\left(\frac{{\mathrm{k}}_1{\mathrm{d}}_1+{\mathrm{k}}_2{\mathrm{d}}_2}{{\mathrm{T}}_1+{\mathrm{T}}_2}\right){\mathrm{T}}_1{\mathrm{T}}_2$                   

(4) $\frac{{\mathrm{k}}_1{\mathrm{d}}_1{\mathrm{T}}_1+{\mathrm{k}}_2{\mathrm{d}}_2{\mathrm{T}}_2}{{\mathrm{k}}_1{\mathrm{d}}_1+{\mathrm{k}}_2{\mathrm{d}}_2}$

A slab consists of two parallel layers of copper and brass of the same thickness and having thermal conductivities in the ratio 1 : 4. If the free face of brass is at 100°C and that of copper at 0°C, the temperature of interface is
1. 80°C               

2. 20°C

3. 60°C               

4. 40°C

Two thin blankets keep more hotness than one blanket of thickness equal to these two. The reason is

(1) Their surface area increases

(2) A layer of air is formed between these two blankets, which is bad conductor

(3) These have more wool

(4) They absorb more heat from outside

Ice formed over lakes has

Wires A and B have identical lengths and have circular cross-sections. The radius of A is twice the radius of B i.e. ${\mathrm{r}}_{\mathrm{A}}=2{\mathrm{r}}_{\mathrm{B}}$ . For a given temperature difference between the two ends, both wires conduct heat at the same rate. The relation between the thermal conductivities is given by

(1) ${\mathrm{K}}_{\mathrm{A}}=4{\mathrm{K}}_{\mathrm{B}}$                     
(2) ${\mathrm{K}}_{\mathrm{A}}=2{\mathrm{K}}_{\mathrm{B}}$
(3) ${\mathrm{K}}_{\mathrm{A}}={\mathrm{K}}_{\mathrm{B}}/2$                   
(4) ${\mathrm{K}}_{\mathrm{A}}={\mathrm{K}}_{\mathrm{B}}/4$

Two identical plates of different metals are joined to form a single plate whose thickness is double the thickness of each plate. If the coefficients of conductivity of each plate are 2 and 3 respectively, then the conductivity of the composite plate will be:
1. 5
2. 2.4
3. 1.5                 
4. 1.2

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