Embibe Experts Solutions for Chapter: Heat Transfer, Exercise 3: Exercise - 3

Two spherical bodies $A$ (radius $6 \mathrm{cm}$) and $B$ (radius $18 \mathrm{cm}$) are at temperatures $T_1$ and $T_2$, respectively. The maximum intensity in the emission spectrum of $A$ is at $500 \mathrm{nm}$ and in that of $B$ is at $1500 \mathrm{nm}$. Considering them to be black bodies, what will be the ratio of the rate of total energy radiated by $A$ to that of $B$?

The temperature of the middle (i.e. second) plate under steady state condition, when three very large plates of same area are kept parallel and close to each other. They are considered as ideal black surfaces and have very high thermal conductivity. The first and third plates are maintained at temperatures $2T$ and $3T$ respectively.

Parallel rays of light of intensity, $I=912 \mathrm{W} {\mathrm{m}}^{-1}$ are incident on a spherical blackbody kept in surroundings of temperature $300 \mathrm{K}$. Take Stefan-Boltzmann's constant, $\sigma =5.7\times {10}^{-8} \mathrm{W} {\mathrm{m}}^{-2} {\mathrm{K}}^{-4}$ and assume that the energy exchange with the surroundings is only through radiation. The final steady-state temperature of the blackbody is close to,

If a piece of metal is heated to temperature $\mathrm{\theta }°\mathrm{C}$ and then allowed cooling in a room which is at temperature ${\mathrm{\theta }}_0°\mathrm{C}$, the graph between the temperature $T$ of the metal and time t will be closest to 

Find Rate of flow of heat through copper rod, where three rods of copper, Brass and steel are welded together to form a $Y$-shaped structure. Area of cross-section of each rod$=4{ \mathrm{cm}}^2$. End of copper rod is maintained at $100°\mathrm{C}$ whereas ends of brass and steel are kept at $0°\mathrm{C}$. Lengths of copper, brass and steel rods are $46, 13$ and $12 \mathrm{cm}$ respectively. The rods are thermally insulated from surroundings except at ends. The thermal conductivities of copper, brass and steel are $0.92, 0.26$ and $0.12 CGS$ units respectively.

A water cooler of storage capacity $120 \mathrm{litres}$ can cool water at a constant rate of $P \mathrm{watts}$. In a closed circulation system (as shown schematically in the figure), the water from the cooler is used to cool an external device that generates constantly $3 \mathrm{kW}$ of heat (thermal load). The temperature of water fed into the device cannot exceed $30 °\mathrm{C}$ and the entire stored $120 \mathrm{litres}$ of water is initially cooled to $10 °\mathrm{C}$. The entire system is thermally insulated. The minimum value of $P$ (in $\mathrm{watts}$) for which the device can be operated for $3 \mathrm{hours}$ is 

The ends $Q$ and $R$ of two thin wires, $PQ$ and $RS,$ are soldered (joined) together. Initially, each of the wire has a length of $1 \mathrm{m}$ at $10 °\mathrm{C}$. Now, the end $P$ is maintained at $10 °\mathrm{C},$ while the end $S$ is heated and maintained at $400 °\mathrm{C}.$ The system is thermally insulated from its surroundings. If the thermal conductivity of wire $PQ$ is twice that of the wire $RS$ and the coefficient of linear thermal expansion of $PQ$ is $1.2\times {10}^{-5} {\mathrm{K}}^{-1}$, the change in length of the wire $PQ$ is

Time taken by a $836 \mathrm{W}$ heater to heat one litre of water from $10 °\mathrm{C}$ to $40 °\mathrm{C}$ is: (specific heat of water is $s=4.2\times {10}^3 \mathrm{J} {\mathrm{kg}}^{-1} {\mathrm{C}}^{-1}$)