Six wire each of cross-sectional area $A$ and length $l$ are combined as shown in the figure. The thermal conductivities of copper and iron are $K_1$ and $K_2$ respectively. The equivalent thermal resistance between points $A$ and $C$ is :-
$\frac{l(K_1+K_2)}{K_1K_2A}$
$\frac{2l(K_1+K_2)}{K_1K_2A}$
$\frac{l}{(K_1+K_2)A}$
$\frac{2l}{(K_1+K_2)A}$
Three rods $A, B$ and $C$ of thermal conductivities $K, 2\,K$ and $4\,K$, cross-sectional areas $A, 2\,A$ and $2\,A$ and lengths $2l, l$ and $l$ respectively are connected as shown in the figure. If the ends of the rods are maintained at temperatures $100^o\,C, 50^o\,C$, and $0^o\,C$ respectively, then the temperature $\theta$ of the junction is ......... $^oC$
The area of the glass of a window of a room is $10\;{m^2}$ and thickness $2mm$. The outer and inner temperature are ${40^o}C$ and ${20^o}C$ respectively. Thermal conductivity of glass in $MKS$ system is $0.2$. The heat flowing in the room per second will be
A partition wall has two layers $A$ and $B$ in contact, each made of a different material. They have the same thickness but the thermal conductivity of layer $A$ is twice that of layer $B$. If the steady state temperature difference across the wall is $60K$, then the corresponding difference across the layer $A$ is ....... $K$
Two spheres of different materials one with double the radius and one-fourth wall thickness of the other, are filled with ice. If the time taken for complete melting ice in the large radius one is $25$ minutes and that for smaller one is $16$ minutes, the ratio of thermal conductivities of the materials of larger sphere to the smaller sphere is
A slab of stone of area $0.36\;m ^2$ and thickness $0.1 \;m$ is exposed on the lower surface to steam at $100^{\circ} C$. A block of ice at $0^{\circ} C$ rests on the upper surface of the slab. In one hour $4.8\; kg$ of ice is melted. The thermal conductivity of slab is .......... $J / m / s /{ }^{\circ} C$ (Given latent heat of fusion of ice $=3.36 \times 10^5\; J kg ^{-1}$)