Two rods of same length, radius and material transfer a given amount of heat in '$t$' seconds when they are joined as shown in fig $(1)$. But when they are joined as shown in fig $(2)$, then they will transfer the same amount of heat under the same conditions in time: (in $t$)

The temperatures of the two outer surfaces of a composite slab,consisting of two materials having coefficients of thermal conductivity $K$ and $2K$ and thickness $x$ and $4x$,respectively,are $T_2$ and $T_1$ $(T_2 > T_1)$. The rate of heat transfer through the slab in a steady state is $\left( \frac{A(T_2 - T_1)K}{x} \right)f$,where $f$ is equal to:

Two identical square metal rods are welded end-to-end as shown in figure $(a)$. $20 \text{ calories}$ of heat flows through them in $4 \text{ minutes}$. If they are joined as shown in figure $(b)$,the same amount of heat will flow in ...... minutes.

$A$ window used to thermally insulate a room from outside consists of two parallel glass sheets each of area $2.6 \,m^2$ and thickness $1 \,cm$ separated by $5 \,cm$ thick stagnant air. In the steady state, the room-glass interface is at $18^{\circ} C$ and the glass-outdoor interface is at $-2^{\circ} C$. If the thermal conductivities of glass and air are respectively $0.8 \,Wm^{-1} K^{-1}$ and $0.08 \,Wm^{-1} K^{-1}$, the rate of flow of heat through the window is (in $\,W$)

Two rods having the same cross-sectional area are used to connect two reservoirs at temperatures $100\,^{\circ}C$ and $0\,^{\circ}C$ as shown. The temperature of the junction is $70\,^{\circ}C$. If the rods are now interchanged,the temperature of the junction will be ......... $^{\circ}C$.

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 $.... ^{\circ} C$.