Three rods of same dimensions have thermal conductivities $3K, 2K$ and $K$. They are arranged as shown in the figure. In the steady state,the temperature of the junction $P$ is:

In Searle's method for finding the thermal conductivity of metals,the temperature gradient along the bar:

Two vessels of different materials are similar in size in every respect. The same quantity of ice filled in them gets melted in $20 \text{ minutes}$ and $30 \text{ minutes}$ respectively. The ratio of their thermal conductivities will be

If the thermal conductivity of aluminum is $0.5 \ cal/cm \cdot s \cdot ^\circ C$,then the temperature gradient required to conduct $10 \ cal/s \cdot cm^2$ in the steady state is ...... $^\circ C/cm$.

$A$ brass boiler has a base area of $0.15\; m^{2}$ and thickness $1.0\; cm$. It boils water at the rate of $6.0\; kg/min$ when placed on a gas stove. Estimate the temperature (in $^oC$) of the part of the flame in contact with the boiler. Thermal conductivity of brass $= 109\; J s^{-1} m^{-1} K^{-1}$; Heat of vaporisation of water $= 2256 \times 10^{3}\; J kg^{-1}$.

The two ends of a rod of length $L$ and a uniform cross-sectional area $A$ are kept at two temperatures $T_1$ and $T_2$ $(T_1 > T_2)$. The rate of heat transfer,$\frac{dQ}{dt}$,through the rod in a steady state is given by: