$A$ body of length $1 \; m$ having a cross-sectional area of $0.75 \; m^2$ has heat flow through it at the rate of $6000 \; J/s$. Find the temperature difference if the thermal conductivity $K = 200 \; J \cdot m^{-1} \cdot s^{-1} \cdot K^{-1}$.

Two conducting cylinders of equal length but different radii are connected in series between two heat baths kept at temperatures $T_1=300 \ K$ and $T_2=100 \ K$,as shown in the figure. The radius of the bigger cylinder is twice that of the smaller one and the thermal conductivities of the materials of the smaller and the larger cylinders are $K_1$ and $K_2$ respectively. If the temperature at the junction of the two cylinders in the steady state is $200 \ K$,then $K_1 / K_2 = . . . . . .$

Two identical rods $AC$ and $CB$ made of two different metals having thermal conductivities in the ratio $2:3$ are kept in contact with each other at the end $C$. $A$ is at $100^{\circ}C$ and $B$ is at $25^{\circ}C$. Then the junction $C$ is at: (in $^{\circ}C$)

One end of a $2.35\,m$ long and $2.0\,cm$ radius aluminium rod $(K = 235\,W\cdot m^{-1}K^{-1})$ is held at $20^{\circ}C$. The other end of the rod is in contact with a block of ice at its melting point. The rate in $kg\cdot s^{-1}$ at which ice melts is (Take latent heat of fusion for ice as $\frac{10}{3} \times 10^5\,J\cdot kg^{-1}$)

Heat current is maximum in which of the following (rods are of identical dimension)?

$A$ room is maintained at $20^{\circ}C$ by a heater of resistance $20 \ \Omega$ connected to $200 \ V$ mains. The temperature is uniform throughout the room and heat is transmitted through a glass window of area $1 \ m^2$ and thickness $0.2 \ cm$. What will be the temperature outside in $^{\circ}C$? Given that thermal conductivity $K = 0.2 \ J/(s \cdot m \cdot K)$ for glass and $J = 4.2 \ J/cal$.