Two bars of thermal conductivities K and 3K and lengths 1 cm and 2 cm respectively have equal cross-sectional area, they are joined lengths wise as shown in the figure. If the temperature at the ends of this composite bar is 0$°\mathrm{C}$ and 100$°\mathrm{C}$ respectively (see figure), then the temperature $\varphi$ of the interface is

(1) 50$°\mathrm{C}$     
               
(2) $\frac{100}{3}°\mathrm{C}$ 

(3) 60$°\mathrm{C}$   
                 
(4) $\frac{200}{3}°\mathrm{C}$ 

A heat flux of 4000 J/s is to be passed through a copper rod of length 10 cm and area of cross-section 100 ${\mathrm{cm}}^2$. The thermal conductivity of copper is 400 W/m$°\mathrm{C}$. The two ends of this rod must be kept at a temperature difference of 
(1) 1$°\mathrm{C}$                

(2) 10$°\mathrm{C}$

(3) 100$°\mathrm{C}$             

(4) 1000$°\mathrm{C}$ 

On a cold morning, a metal surface will feel colder to touch than a wooden surface because 

(1) Metal has high specific heat

(2) Metal has high thermal conductivity

(3) Metal has low specific heat

(4) Metal has low thermal conductivity

The coefficient of thermal conductivity of copper is nine times that of steel. In the composite cylindrical bar shown in the figure. What will be the temperature at the junction of copper and steel 

(a) 75$°\mathrm{C}$
(b) 67$°\mathrm{C}$
(c) 33$°\mathrm{C}$
(d) 25$°\mathrm{C}$

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 $°\mathrm{C}$