An insulated container is filled with ice at $0\,^oC$ , and another container is filled with water that is continuously boiling at $100\,^oC$ . In series of experiments, the containers are connected by various thick metal rods that pass through the walls of container as shown in the figure

In the experiment $I$ : a copper rod is used and all ice melts in $20$ minutes.

In the experiment $II$ : a steel rod of identical dimensions is used and all ice melts in $80$ minutes.

In the experiment $III$ : both the rods are used in series and all ice melts in $t_{10}$ minutes.

In the experiment $IV$ : both rods are used in parallel and all ice melts in $t_{20}$ minutes.

- A
The value of $t_{10}$ is $100$ minutes

- B
The value of $t_{10}$ is $50$ minutes

- C
The value of $t_{20}$ is $32$ minutes

- D
The value of $t_{20}$ is $8$ minutes

Four rods of identical cross-sectional area and made from the same metal form the sides of square. The temperature of two diagonally opposite points and $T$ and $\sqrt 2 $ $T$ respective in the steady state. Assuming that only heat conduction takes place, what will be the temperature difference between other two points

Two rods $A$ and $B$ of different materials are welded together as shown in figure.Their thermal conductivities are $K_1$ and $K_2$ The thermal conductivity of the composite rod will be

- [NEET 2017]

The coefficient of thermal conductivity of copper is nine times that of steel. In the composite cylindrical bar shown in the figure. What will be the temperature at the junction of copper and steel ....... $^oC$

A cylindrical steel rod of length $0.10 \,m$ and thermal conductivity $50 \,Wm ^{-1} K ^{-1}$ is welded end to end to copper rod of thermal conductivity $400 \,Wm ^{-1} K ^{-1}$ and of the same area of cross-section but $0.20 \,m$ long. The free end of the steel rod is maintained at $100^{\circ} C$ and that of the copper rod at $0^{\circ} C$. Assuming that the rods are perfectly insulated from the surrounding, the temperature at the junction of the two rods is ................... $^{\circ} C$

- [KVPY 2012]

Three rods made of the same material and having the same cross section have been joined as shown in the figure. Each rod is of the same length. The left and right ends are kept at ${0^o}C$ and ${90^o}C$ respectively. The temperature of the junction of the three rods will be ...... $^oC$

- [IIT 2001]