Three identical rods $AB$,$CD$ and $PQ$ are joined as shown. $P$ and $Q$ are midpoints of $AB$ and $CD$ respectively. Ends $A, B, C$ and $D$ are maintained at $0^{\circ} C, 100^{\circ} C, 30^{\circ} C$ and $60^{\circ} C$ respectively. The direction of heat flow in $PQ$ is

$A$ 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?

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 $P$)

Fill in the blanks:
$(a)$ $0.49 \frac{\text{cal}}{\text{cm} \cdot \text{K} \cdot \text{s}} = \dots \frac{\text{J}}{\text{m} \cdot \text{K} \cdot \text{s}}$
$(b)$ If the rate of emission of heat of a substance is less than its rate of absorption,then its temperature $\dots$.
$(c)$ The rate of emission of heat of a substance is directly proportional to $\dots$ of temperature of it and surroundings.

$A$ thin piece of thermal conductor of constant thermal conductivity,insulated on the lateral sides,connects two reservoirs which are maintained at temperatures $T_{1}$ and $T_{2}$ as shown in the figure. Assuming that the system is in a steady state,which of the following plots best represents the dependence of the rate of change of entropy on the ratio $T_{1} / T_{2}$?

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 ....... $hr$.