Embibe Experts Solutions for Chapter: Heat Transfer, Exercise 1: Exercise - 1

One end of a steel rod $\left(K=46 \mathrm{J} {\mathrm{s}}^{-1} {\mathrm{m}}^{-1} °{\mathrm{C}}^{-1}\right)$ of length $1.0 \mathrm{m}$ is kept in ice at $0 °\mathrm{C}$ and the other end is kept in boiling water at $100 °\mathrm{C}$. The area of cross-section of the rod is $0.04 {\mathrm{cm}}^2$. Assuming no heat loss to the atmosphere, find the mass of the melting per second. Latent heat of fusion of ice$=3.36\times {10}^5 \mathrm{J} {\mathrm{kg}}^{-1}$.

A semicircular rod is joined at its end to a straight rod of the same material and the same cross-sectional area. The straight rod forms a diameter of the other rod. The junctions are maintained at different temperatures. Find the ratio of the heat transferred through a cross section of the semicircular rod to the heat transferred through a cross section of the straight rod in a given time.

A hollow metallic sphere of radius $20 \mathrm{cm}$ surrounds a concentric metallic sphere of radius $5 \mathrm{cm}$. The space between the two-sphere is filled with nonmetallic material. The inner and outer spheres are maintained at $50 °\mathrm{C}$ and $10 °\mathrm{C}$, respectively, and it is found that $100 \mathrm{J}$ of heat passes from the inner sphere to the outer sphere per second. Find the thermal conductivity of the material between the spheres.

A metal rod of cross-sectional area $1.0 {\mathrm{cm}}^2$ is being heated at one end. At one time, the temperature gradient is $5.0 °\mathrm{C} {\mathrm{cm}}^{-1}$ at cross-section $A$ and is $2.5 °\mathrm{C} {\mathrm{cm}}^{-1}$ at cross-section $B$. Calculate the rate at which the temperature is increasing in the part $AB$ of the rod. The heat capacity of the part $AB=0.40 \mathrm{J} °{\mathrm{C}}^{-1}$ thermal conductivity of the material of the rod $=$$200 \mathrm{W} {\mathrm{m}}^{-1} °{\mathrm{C}}^{-1}$. Neglect any loss of heat to the atmosphere.

A boiler is made of a copper plate $2.4 \mathrm{mm}$ thick with an inside coating of a $0.2 \mathrm{mm}$ thick layer of tin. The surface area exposed to gases at $700°\mathrm{C}$ is $400 {\mathrm{cm}}^2.$ The maximum amount of steam that could be generated per hour at atmospheric pressure is (${\mathrm{K}}_{\mathrm{Cu}}=0.9 \mathrm{cal}/\mathrm{cm}/\mathrm{s}/{}^{\circ }\mathrm{C}$ and ${\mathrm{K}}_{\text{tin }}=0.15\mathrm{cal}/\mathrm{cm}/\mathrm{s}/{}^{\circ }\mathrm{C}$   and $L_{\text{steam }}=540 \mathrm{cal} {\mathrm{g}}^{-1}$):

Three separate segments of equal area $A_1, A_2$ and $A_3$ are shown in the energy distribution curve of blackbody radiation. If $n_1, n_2$and $n_3$ are a number of photons emitted per unit time corresponding to each area segment respectively then: 

Which of the law can be understood in terms of Stefan's law?

A hot liquid is kept in a big room. According to Newton's law of cooling rate of cooling of liquid (represented as $y$) is plotted against its temperature $T$. Which of the following curves may represent the plot?