Two rods (one semi-circular and one straight) are made of the same material and have the same cross-sectional area. They are joined as shown in the figure. Points $A$ and $B$ are maintained at different temperatures. The ratio of the heat current flowing through the semi-circular rod to that flowing through the straight rod in a given time is:

Two plates of equal area are placed in contact. Their thicknesses are $2$ and $3$ units respectively. The temperature of the outer surface of the first plate is $-25^{\circ}C$ and the temperature of the outer surface of the second plate is $25^{\circ}C$. Find the temperature of the contact surface if: $(a)$ they are made of the same material,$(b)$ their thermal conductivities are in the ratio $2:3$.

$A$ 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 ....... $^{\circ}C$.

Two metal rods $1$ and $2$ of same lengths have same temperature difference between their ends. Their thermal conductivities are $K_1$ and $K_2$ and cross-sectional areas are $A_1$ and $A_2$,respectively. If the rate of heat conduction in rod $1$ is four times that in rod $2$,then:

One end of a metal rod of length $1.0 \ m$ and area of cross-section $100 \ cm^2$ is maintained at $100^{\circ}C$. If the other end of the rod is maintained at $0^{\circ}C$,the quantity of heat transmitted through the rod per minute is (Coefficient of thermal conductivity of the material of the rod = $100 \ W/m-K$).

The ends of two rods of different materials with their thermal conductivities,radii of cross-sections,and lengths all in the ratio $1:2$ are maintained at the same temperature difference. If the rate of flow of heat in the larger rod is $4 \; cal/sec$,the rate of flow of heat in the shorter rod in $cal/sec$ will be: