Three rods of the same dimensions have thermal conductivities $3k, 2k$ and $k$. They are arranged as shown,with their ends at $100\,^{\circ}C, 50\,^{\circ}C$ and $0\,^{\circ}C$. The temperature of their junction is

The coefficient of thermal conductivity depends upon

Two plates of equal area are placed in contact with each other. Their thicknesses are $2.0 \ cm$ and $5.0 \ cm$. The temperature of the outer surface of the first plate is $-20^{\circ}C$ and the temperature of the outer surface of the second plate is $20^{\circ}C$. If the ratio of their thermal conductivities is $2:5$,find the temperature of the contact surface in $^{\circ}C$.

$A$ body of length $1 \; m$ having a cross-sectional area of $0.75 \; m^2$ has heat flow through it at the rate of $6000 \; J/s$. Find the temperature difference if the thermal conductivity $K = 200 \; J \cdot m^{-1} \cdot s^{-1} \cdot K^{-1}$.

$A$ rectangular ice box of total surface area of $1000 \,cm^2$ initially contains $1.5 \,kg$ of ice at $0^{\circ}C$. If the thickness of the walls of the box is $2 \,mm$ and the temperature outside the box is $42^{\circ}C$, then the mass of the ice remaining in the box after $160 \,minutes$ is (Thermal conductivity of the material of the box $= 10^{-2} \,W m^{-1} K^{-1}$ and latent heat of the fusion of ice $= 336 \times 10^3 \,J kg^{-1}$) (in $kg$)

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: