A cylindrical metallic rod in thermal contact with two reservoirs of heat at its two ends conducts an amount of heat $Q$ in time $t$. The metallic rod is melted and the material is formed into a rod of half the radius of the original rod. What is the amount of heat conducted by the new rod, when placed in thermal contact with the two reservoirs in time $t$ ?
$\frac{Q}{4}\;$
$\;\frac{Q}{{16}}$
$\;2Q$
$\;\frac{Q}{2}$
Two rods one made of copper and other made of steel of the same length and same cross sectional area are joined together. The thermal conductivity of copper and steel are $385\,J\,s ^{-1}\,K ^{-1}\,m ^{-1}$ and $50\,J\,s ^{-1}\,K ^{-1}\,m ^{-1}$ respectively. The free ends of copper and steel are held at $100^{\circ}\,C$ and $0^{\circ}\,C$ respectively. The temperature at the junction is, nearly $.......^{\circ}\,C$
$A$ wall is made up of two layers $A$ and $B$ . The thickness of the two layers is the same, but materials are different. The thermal conductivity of $A$ is double than that of $B$ . In thermal equilibrium the temperature difference between the two ends is ${36^o}C$. Then the difference of temperature at the two surfaces of $A$ will be ....... $^oC$
Two identical rods of copper and iron are coated with wax uniformly. When one end of each is kept at temperature of boiling water, the length upto which wax melts are $8.4cm$ and $4.2cm$ respectively. If thermal conductivity of copper is $0.92$ , then thermal conductivity of iron is
Two identical square rods of metal are welded end to end as shown in figure $(i)$ , $20$ calories of heat flows through it in $4$ minutes. If the rods are welded as shown in figure $(ii)$, the same amount of heat will flow through the rods in ....... $\min.$
One end of a thermally insulated rod is kept at a temperature $T_1$ and the other at $T_2$ . The rod is composed of two sections of length $l_1$ and $l_2$ and thermal conductivities $K_1$ and $K_2$ respectively. The temperature at the interface of the two section is