A cylindrical rod having temperature ${T_1}$ and ${T_2}$ at its ends. The rate of flow of heat is ${Q_1}$ $cal/sec$. If all the linear dimensions are doubled keeping temperature constant then rate of flow of heat ${Q_2}$ will be
$4{Q_1}$
$2{Q_1}$
$\frac{{{Q_1}}}{4}$
$\frac{{{Q_1}}}{2}$
Three rods of the same dimensions have thermal conductivities $3k, 2k$ and $k$. They are arranged as shown, with their ends at $100\,^oC, 50\,^oC$ and $0\,^oC$. The temperature of their junction is
The temperature of hot and cold end of a $20cm$ long rod in thermal steady state are at ${100^o}C$ and ${20^o}C$ respectively. Temperature at the centre of the rod is...... $^oC$
Bottom of a lake is at $0^{\circ} C$ and atmospheric temperature is $-20^{\circ} C$. If $1 cm$ ice is formed on the surface in $24 \,h$, then time taken to form next $1 \,cm$ of ice is ......... $h$
A copper pipe of length $10 \,m$ carries steam at temperature $110^{\circ} C$. The outer surface of the pipe is maintained at a temperature $10^{\circ} C$. The inner and outer radii of the pipe are $2 \,cm$ and $4 \,cm$, respectively. The thermal conductivity of copper is $0.38 kW / m /{ }^{\circ} C$. In the steady state, the rate at which heat flows radially outward through the pipe is closest to ............. $\,kW$
Two rectangular blocks, having identical dimensions, can be arranged either in configuration $I$ or in configuration $II$ as shown in the figure. One of the blocks has thermal conductivity $k$ and the other $2k$. The temperature difference between the ends along the $x-$ axis is the same in both the configurations. It takes $9s$ to transport a certain amount of heat from the hot end to the cold end in the configuration $I$. The time to transport the same amount of heat in the configuration $II$ is .......... $\sec$