$A$ metal cooking pot has a base area of $0.2 \,m^2$ and a thickness of $2.0 \,cm$. It boils water at a rate of $3.0 \,kg/min$ when placed on a hot plate. What is the temperature of the part of the hot plate in contact with the pot (in $^{\circ} C$)? [Thermal conductivity of metal is $120 \,J s^{-1} m^{-1} K^{-1}$, latent heat of vaporisation of water is $2 \times 10^6 \,J/kg$]

$A$ cylindrical rod has temperatures $T_1$ and $T_2$ at its ends. The rate of flow of heat is $Q_1 \text{ cal s}^{-1}$. If the length and radius of the rod are doubled while keeping the temperatures constant,then the new rate of flow of heat $Q_2$ will be:

$A$ metal rod of length $10 \text{ cm}$ and area of cross-section $2.8 \times 10^{-4} \text{ m}^2$ is covered with a non-conducting substance. One end of it is maintained at $80^{\circ} \text{C}$,while the other end is put in ice at $0^{\circ} \text{C}$. It is found that $20 \text{ g}$ of ice melts in $5 \text{ min}$. The thermal conductivity of the metal in $\text{J s}^{-1} \text{ m}^{-1} \text{ K}^{-1}$ is (Latent heat of ice is $80 \text{ cal g}^{-1}$.)

In a steady state, the graph between temperature $(\theta)$ and distance $(x)$ from the hot end is:

On a winter morning,a metal surface feels colder to the touch than a wooden surface because:

Consider two rods $1$ and $2$ of same length $L$. They have different specific heats $(C_1, C_2)$, thermal conductivities $(K_1, K_2)$ and area of cross-section $(A_1, A_2)$ respectively. Both the rods have temperatures $(T_1, T_2)$ at their ends. If their rate of loss of heat due to conduction is equal, then