$A$ wall has two layers $A$ and $B$ each made of different materials,both layers have the same thickness. The thermal conductivity of material $A$ is twice that of $B$. Under thermal equilibrium,the temperature difference across wall $B$ is $36^{\circ}C$. The temperature difference across wall $A$ is ....... $^{\circ}C$.

$A$ metallic rod of cross-sectional area $9.0 \, cm^2$ and length $0.54 \, m$,with the surface insulated to prevent heat loss,has one end immersed in boiling water and the other in an ice-water mixture. The heat conducted through the rod melts the ice at the rate of $1 \, g$ for every $33 \, s$. The thermal conductivity of the rod is ....... $W m^{-1} K^{-1}$.

Which of the following material properties is most suitable for a cooking utensil?

Same quantity of ice is filled in each of the two metal containers $P$ and $Q$ having the same size, shape, and wall thickness but made of different materials. The containers are kept in identical surroundings. The ice in $P$ melts completely in time $t_{1}$ whereas in $Q$ it takes a time $t_{2}$. The ratio of thermal conductivities of the materials of $P$ and $Q$ is

In a steady state, the graph between temperature $(\theta)$ and distance $(x)$ from the hot end is:

$A$ 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 $J = 4.2 \ J/cal$.