Two plates of equal area are placed in series. The ratios of their thicknesses and thermal conductivities are both $2:3$. The temperature of the outer surface of one plate is $100 ^\circ C$ and that of the other is $0 ^\circ C$. The temperature of the common surface is ....... $^\circ C$.

The two ends of a rod of length $L$ and a uniform cross-sectional area $A$ are kept at two temperatures $T_1$ and $T_2$ $(T_1 > T_2)$. The rate of heat transfer,$\frac{dQ}{dt}$,through the rod in a steady state is given by:

Three rods of same dimensions have thermal conductivities $3K, 2K$ and $K$. They are arranged as shown with their ends at $100^{\circ}C, 50^{\circ}C$ and $0^{\circ}C$. The temperature of the junction is

An ice cube of dimensions $60\,cm \times 50\,cm \times 20\,cm$ is placed in an insulation box of wall thickness $1\,cm$. The box keeping the ice cube at $0^{\circ}C$ temperature is brought to a room of temperature $40^{\circ}C$. The rate of melting of ice is approximately. (Latent heat of fusion of ice is $3.4 \times 10^{5}\,J\,kg^{-1}$ and thermal conductivity of insulation wall is $0.05\,W\,m^{-1\circ}C^{-1}$)

Two walls of thickness $d_1$ and $d_2$ and thermal conductivities $k_1$ and $k_2$ are in contact. In the steady state,the temperatures of the outer surfaces are $T_1$ and $T_2$. Find the temperature of the common interface.

The area of a glass window is $10 \ m^2$ and its thickness is $2 \ mm$. The outside and inside temperatures are $40^{\circ}C$ and $20^{\circ}C$ respectively. The thermal conductivity in $MKS$ units is $0.2$. The heat conducted per second into the room is ......