The ratio of thermal conductivity of two rods of different material is $5 : 4$ . The two rods of same area of cross-section and same thermal resistance will have the lengths in the ratio

Ice starts forming in lake with water at ${0^o}C$ and when the atmospheric temperature is $ - {10^o}C$. If the time taken for $1 \;cm$ of ice be $7$ hours, then the time taken for the thickness of ice to change from $1\; cm$ to $2\; cm$ is

The coefficients of thermal conductivity of copper, mercury and glass are respectively $Kc, Km$ and $Kg$ such that $Kc > Km > Kg$ . If the same quantity of heat is to flow per second per unit area of each and corresponding temperature gradients are $Xc, Xm$ and $Xg$ , then

Two cylinders $P$ and $Q$ have the same length and diameter and are made of different materials having thermal conductivities in the ratio $2 : 3$ . These two cylinders are combined to make a cylinder. One end of $P$ is kept at $100°C$  and another end of $Q$ at $0°C$ . The temperature at the interface of $P$ and $Q$ is ...... $^oC$

Four conducting rods are joined to make a square. All rods are identical and ends $A, B$ and $C$ are maintained at given temperatures. choose $INCORRECT$ statement for given arrangement in steady state. (value of $\frac {KA}{L}$ is $1\frac{J}{{{S^o}C}}$ , symbols , have their usual meaning) 

$A$ metal rod of length $2$$m$ has cross sectional areas $2A$ and $A$ as shown in figure. The ends are maintained at temperatures $100°C$ and $70°C$ . The temperature at middle point $C$ is...... $^oC$