A slab consists of two parallel layers of two different materials of same thickness having thermal conductivities ${\mathrm{K}}_1$ and ${\mathrm{K}}_2$. The equivalent conductivity of the combination is

(1) ${\mathrm{K}}_1+{\mathrm{K}}_2$           

(2) $\frac{{\mathrm{K}}_1+{\mathrm{K}}_2}{2}$

(3) $\frac{2{\mathrm{K}}_1{\mathrm{K}}_2}{{\mathrm{K}}_1+{\mathrm{K}}_2}$         

(4) $\frac{{\mathrm{K}}_1+{\mathrm{K}}_2}{2{\mathrm{K}}_1{\mathrm{K}}_2}$

There are two identical vessels filled with equal amounts of ice. The vessels are of different metals., If the ice melts in the two vessels in 20 and 35 minutes respectively, the ratio of the coefficients of thermal conductivity of the two metals is

(1) 4 : 7                   

(2) 7 : 4

(3) 16 :49                 

(4) 49 : 16

Heat current is maximum in which of the following (rods are of identical dimension) ?

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) $\frac{2}{3}\mathrm{K}$

Two rods having thermal conductivity in the ratio of 5 : 3 having equal lengths and equal cross-sectional area are joined by face to face. If the temperature of the free end of the first rod is 100$°\mathrm{C}$ and free end of the second rod is 20$°\mathrm{C}$. Then temperature of the junction is

(1) 70 $°\mathrm{C}$                   

(2) 50 $°\mathrm{C}$

(3) 50 $°\mathrm{C}$                  

(4) 90 $°\mathrm{C}$

Woollen clothes are used in winter season because woollen clothes

(1) Are good sources for producing heat

(2) Absorb heat from surroundings

(3) Are bad conductors of heat

(4) Provide heat to body continuously

Two metal cubes and of same size are arranged as shown in the figure. The extreme ends of the combination are maintained at the indicated temperatures. The arrangement is thermally insulated. The coefficients of thermal conductivity of A and B are 300 W/m$°\mathrm{C}$ and 200 W/m$°\mathrm{C}$, respectively. After steady state is reached, the temperature of the interface will be 

(1) 45$°\mathrm{C}$
(2) 90$°\mathrm{C}$
(3) 30$°\mathrm{C}$
(4) 60$°\mathrm{C}$

A cylindrical rod having temperature ${\mathrm{T}}_1$ and ${\mathrm{T}}_2$ at its ends. The rate of flow of heat is ${\mathrm{Q}}_1$ cal/sec. If all the linear dimensions are doubled keeping temperature constant then rate of flow of heat ${\mathrm{Q}}_2$ will be
(a) $4{\mathrm{Q}}_1$           (b) $2{\mathrm{Q}}_1$
(c)$\frac{{\mathrm{Q}}_1}{4}$            (d) $\frac{{\mathrm{Q}}_1}{2}$

A body of length 1m having cross sectional area 0.75 ${\mathrm{m}}^2$ has heat flow through it at the rate of 6000 Joule/sec. Then find the temperature difference if K = 200 ${\mathrm{Jm}}^{-1}{\mathrm{K}}^{-1}$ 

(a) 20°C                     (b) 40°C
(c) 80°C                     (d) 100°C

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.