A large cylindrical rod of length $L$ is made by joining two identical rods of copper and steel of length $(\frac {L}{2})$ each . The rods are completely insulated from the surroundings. If the free end of copper rod is maintained at $100\,^oC$ and that of steel at $0\,^oC$ then the temperature of junction is........$^oC$ (Thermal conductivity of copper is $9\,times$ that of steel)
$90$
$50$
$10$
$67$
One end of a metal rod of length $1.0 m$ and area of cross section $100c{m^2}$ is maintained at ${100^o}C.$If the other end of the rod is maintained at ${0^o}C$, the quantity of heat transmitted through the rod per minute is (Coefficient of thermal conductivity of material of rod =$100W/m-K$)
The ends $\mathrm{Q}$ and $\mathrm{R}$ of two thin wires, $\mathrm{PQ}$ and $RS$, are soldered (joined) togetker. Initially each of the wires has a length of $1 \mathrm{~m}$ at $10^{\circ} \mathrm{C}$. Now the end $\mathrm{P}$ is maintained at $10^{\circ} \mathrm{C}$, while the end $\mathrm{S}$ is heated and maintained at $400^{\circ} \mathrm{C}$. The system is thermally insulated from its surroundings. If the thermal conductivity of wire $\mathrm{PQ}$ is twice that of the wire $RS$ and the coefficient of linear thermal expansion of $P Q$ is $1.2 \times 10^{-5} \mathrm{~K}^{-1}$, the change in length of the wire $\mathrm{PQ}$ is
Three identical rods $AB$, $CD$ and $PQ$ are joined as shown. $P$ and $Q$ are mid points of $AB$ and $CD$ respectively. Ends $A, B, C$ and $D$ are maintained at $0^o C, 100^o C, 30^o C$ and $60^o C$ respectively. The direction of heat flow in $PQ$ is
Temperature of water at the surface of lake is $ - {20^o}C$ Then temperature of water just below the lower surface of ice layer is ...... $^oC$
Two rods having thermal conductivity in the ratio of $5 : 3$ having equal lengths and equal cross-sectional area are joined by face to face. If the temperature of the free end of the first rod is $100°C$ and free end of the second rod is $20°C$ . Then temperature of the junction is...... $^oC$