Consider a compound slab consisting of two different materials having equal thickness and thermal conductivities $K$ and $2K$ respectively. The equivalent thermal conductivity of the slab is

The ratio of thermal conductivities of two materials is $1 : 2$. If the ratio of the lengths of the rods of these materials is $1 : 2$ and the ratio of their cross-sectional areas is $2 : 1$,then the ratio of their thermal resistances is:

Six identical conducting rods are joined as shown in the figure. Points $A$ and $D$ are maintained at $100^{\circ} C$ and $10^{\circ} C$ respectively. The temperature of junction $C$ will be $.... ^{\circ} C$.

Three rods $AB$,$BC$,and $BD$ made of the same material and having the same cross-section have been joined as shown in the figure. The ends $A$,$C$,and $D$ are held at temperatures of $20^{\circ} C$,$80^{\circ} C$,and $80^{\circ} C$ respectively. If each rod is of the same length,then the temperature at the junction $B$ of the three rods is: (in $^{\circ} C$)

$A$ ring consisting of two parts $ADB$ and $ACB$ of same conductivity $k$ carries an amount of heat $H$. The $ADB$ part is now replaced with another metal keeping the temperatures $T_1$ and $T_2$ constant. The heat carried increases to $2H$. What should be the conductivity of the new $ADB$ part? Given $\frac{l_{ACB}}{l_{ADB}} = 3$.

Five identical rods are joined as shown in the figure. Points $A$ and $C$ are maintained at temperatures $120^\circ C$ and $20^\circ C$ respectively. The temperature of junction $B$ will be....... $^\circ C$