What are the modes of heat transfer due to a temperature difference?

The only possibility of heat flow in a thermos flask is through its cork,which is $75 \ cm^2$ in area and $5 \ cm$ thick. Its thermal conductivity is $0.0075 \ cal/(cm \cdot s \cdot ^\circ C)$. The outside temperature is $40^\circ C$ and the latent heat of fusion of ice is $80 \ cal/g$. The time taken by $500 \ g$ of ice at $0^\circ C$ in the flask to melt into water at $0^\circ C$ is ....... $hr$.

$A$ long metallic bar is carrying heat from one of its ends to the other end under steady-state. The variation of temperature $\theta$ along the length $x$ of the bar from its hot end is best described by which of the following figures?

$A$ cylinder of radius $R$ made of a material of thermal conductivity $K_1$ is surrounded by a cylindrical shell of inner radius $R$ and outer radius $2R$ made of material of thermal conductivity $K_2$. The two ends of the combined system are maintained at two different temperatures. There is no loss of heat across the cylindrical surface and the system is in steady state. The effective thermal conductivity of the system is

$A$ wall with a cavity consists of two layers of brick separated by a layer of air. All three layers have the same thickness,and the thermal conductivity of the brick is much greater than that of air. The left layer is at a higher temperature than the right layer,and a steady-state condition exists. Which of the following graphs correctly predicts the variation of temperature $T$ with distance $d$ inside the cavity?

Power radiated by a black body at temperature $T_1$ is $P$ and it radiates maximum energy at a wavelength $\lambda_1$. If the temperature of the black body is changed from $T_1$ to $T_2$, it radiates maximum energy at a wavelength $\frac{\lambda_1}{2}$. The power radiated at $T_2$ is (in $P$)