At a common temperature, a block of wood and a block of metal feel equally cold or hot. The temperatures of block of wood and block of metal are

Two rectangular blocks $A$ and $B$ of different metals have same length and same area of cross-section. They are kept in such a way that their cross-sectional area touch each other. The temperature at one end of $A$ is $100°C$ and that of $B$ at the other end is $0°C$ . If the ratio of their thermal conductivity is $1 : 3$ , then under steady state, the temperature of the junction in contact will be …….. $^oC$

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.

Three rods of identical area of cross-section and made from the same metal form the sides of an isosceles triangle $ABC$, right angled at $B$. The points $A$ and $B$ are maintained at temperatures $T$ and $\sqrt 2 T$ respectively. In the steady state the temperature of the point C is ${T_C}$. Assuming that only heat conduction takes place, $\frac{{{T_C}}}{T}$ is equal to

Which of the following circular rods. (given radius $ r$ and length $l$ ) each made of the same material as whose ends are maintained at the same temperature will conduct most heat