Two rods have thermal conductivities $K$ and $3K$ and lengths $1 \ cm$ and $2 \ cm$ respectively. Their cross-sectional areas are equal. They are joined in series as shown in the figure. If the temperatures of the outer ends of this composite rod are $0^{\circ}C$ and $100^{\circ}C$ respectively,find the junction temperature $\phi$ in $^{\circ}C$.

Consider two rods of same length and different specific heats $(S_{1}, S_{2})$,conductivities $(K_{1}, K_{2})$ and area of cross-sections $(A_{1}, A_{2})$ and both having temperatures $T_{1}$ and $T_{2}$ at their ends. If the rate of loss of heat due to conduction is equal,then:

One end of a metal rod of length $1.0 \ m$ and area of cross-section $100 \ cm^2$ is maintained at $100^{\circ}C$. If the other end of the rod is maintained at $0^{\circ}C$,the quantity of heat transmitted through the rod per minute is (Coefficient of thermal conductivity of the material of the rod = $100 \ W/m-K$).

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

Two rods,one made of copper and the other made of steel,of the same length and same cross-sectional area,are joined together. The thermal conductivities of copper and steel are $385 \, W \, m^{-1} \, K^{-1}$ and $50 \, W \, m^{-1} \, K^{-1}$ 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 $.......^{\circ} \, C$.

The temperature of the water of a pond is $0^{\circ} C$ while that of the surrounding atmosphere is $-20^{\circ} C$. If the density of ice is $\rho$, the coefficient of thermal conductivity is $k$, and the latent heat of melting is $L$, then the thickness $Z$ of the ice layer formed increases as a function of time $t$ as: