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

In a closed room,heat transfer takes place by

$A$ hot black body emits energy at the rate of $16 \ J \ m^{-2} \ s^{-1}$ and its most intense radiation corresponds to $20,000 \ \mathring{A}$. When the temperature of this body is further increased and its most intense radiation corresponds to $10,000 \ \mathring{A}$,then the energy radiated in $J \ m^{-2} \ s^{-1}$ will be

Three rods of Copper,Brass,and Steel are welded together to form a $Y$ shaped structure. The area of cross-section of each rod is $4 \ cm^2$. The end of the copper rod is maintained at $100^\circ C$,whereas the ends of the brass and steel rods are kept at $0^\circ C$. The lengths of the copper,brass,and steel rods are $46 \ cm$,$13 \ cm$,and $12 \ cm$ respectively. The rods are thermally insulated from the surroundings except at the ends. The thermal conductivities of copper,brass,and steel are $0.92$,$0.26$,and $0.12 \ CGS$ units respectively. The rate of heat flow through the copper rod is ....... $cal \ s^{-1}$.

$A$ heated body maintained at $T \ K$ emits thermal radiation of total energy $E$ with a maximum intensity at frequency $v$. The emissivity of the material is $0.5$. If the temperature of the body is increased and maintained at temperature $3T \ K$,then:
$(i)$ The maximum intensity of the emitted radiation will occur at frequency $v/3$.
$(ii)$ The maximum intensity of the emitted radiation will occur at frequency $3v$.
$(iii)$ The total energy of emitted radiation will become $81E$.
$(iv)$ The total energy of emitted radiation will become $27E$.

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.