Five rods of same dimensions are arranged as shown in the figure. They have thermal conductivities $K1, K2, K3, K4$ and $K5$ . When points $A$ and $B$ are maintained at different temperatures, no heat flows through the central rod if

Two materials having coefficients of thermal conductivity $3K$ and $K$ and thickness $d$ and $3d$, respectively, are joined to form a slab as shown in the figure. The temperatures of the outer surfaces are  $\theta_2$ and $\theta_1$ respectively  $\left( {\theta _2} > {\theta _1} \right)$ . The temperature at the interface is

Objects $A$ and $B$ that are initially separated from each other and well isolated from their surroundings are then brought into thermal contact. Initially $T_A= 0^oC$ and $T_B = 100^oC$. The specific heat of $A$ is less than the specific heat of $B$. After some time, the system comes to an equilibrium state. The final temperatures are :

One end of a thermally insulated rod is kept at a temperature $T_1$ and the other at $T_2$ . The rod is composed of two sections of length $l_1$ and $l_2$ and thermal conductivities $K_1$ and $K_2$ respectively. The temperature at the interface of the two section is

A brass boiler has a base area of $0.15\; m ^{2}$ and thickness $1.0\; cm .$ It boils water at the rate of $6.0\; kg / min$ when placed on a gas stove. Estimate the temperature (in $^oC$) of the part of the flame in contact with the boiler. Thermal conductivity of brass $=109 \;J s ^{-1} m ^{-1} K ^{-1} ;$ Heat of vaporisation of water $=2256 \times 10^{3}\; J kg ^{-1}$

Two rods one made of copper and other made of steel of the same length and same cross sectional area are joined together. The thermal conductivity of copper and steel are $385\,J\,s ^{-1}\,K ^{-1}\,m ^{-1}$ and $50\,J\,s ^{-1}\,K ^{-1}\,m ^{-1}$ respectively. The free ends of copper and steel are held at $100^{\circ}\,C$ and $0^{\circ}\,C$ respectively. The temperature at the junction is, nearly $.......^{\circ}\,C$