B M Sharma Solutions for Chapter: Transmission of Heat, Exercise 2: CONCEPT APPLICATION EXERCISE

A refrigerator door is $150 \mathrm{cm}$ high, $80 \mathrm{cm}$ wide, and $6 \mathrm{cm}$ thick. If the coefficient of conductivity is $0.0005\mathrm{cal}/\mathrm{cm}-\mathrm{s}-{}^{\circ }\mathrm{C}$, and the inner and outer surfaces are at $0°\mathrm{C}$ and $30°\mathrm{C}$, respectively, what is the heat loss per minute through the door, in calories?

The only possibility of heat flow in a thermos flask is through its cork which is $75{ \mathrm{cm}}^2$ in area and $5 \mathrm{cm}$ thick. Its thermal conductivity is $0.0075 \mathrm{cal}/\mathrm{cm}-\sec -{}^{\circ }\mathrm{C}$. The outside temperature is $40°\mathrm{C}$ and latent heat of ice is $80 \mathrm{cal}-{\mathrm{g}}^{-1}$. Find the time taken by $500 \mathrm{g}$ of ice at $0°\mathrm{C}$ in the flask to melt into water at $0{}^{\circ }\mathrm{C}$.

The opposite faces of a cubical block of iron of crosssection $4.0{ \mathrm{cm}}^2$ are kept in contact with steam and melting ice. Calculate the quantity of ice melted in $10$ minutes ($k$ for iron $=0.2$ C.G.S. units).

A thermocole cubical icebox of side $30 \mathrm{cm}$ has a thickness of $5.0 \mathrm{cm}$. If $4.0 \mathrm{kg}$ of ice is put in the box, estimate the amount of ice remaining after $6 \mathrm{h}$. The outside temperature is $45°\mathrm{C}$ and coefficient of thermal conductivity of thermocole $=0.01 \mathrm{J}/\mathrm{sm}-{}^{\circ }\mathrm{C}$. Given heat of fusion of water $=335\times {10}^3 \mathrm{J}/\mathrm{kg}$.

A uniform copper bar $100 \mathrm{cm}$ long is insulated on side, and has its ends exposed to ice and steam respectively. If there is a layer of water $0.1 \mathrm{mm}$ thick at each end, calculate the temperature gradient in the bar. $K_{\mathrm{Cu}}=1.04$ and $K_{\mathrm{water}}=0.0014$ in C.G.S. units.

One end of a brass rod of length $2.0 \mathrm{m}$ and cross-section $1{ \mathrm{cm}}^2$ is kept in stream at $100°\mathrm{C}$ and the other end in ice at $0°\mathrm{C}$. The lateral surface of the rod is covered by heat insulator. Determine the amount of ice melting per minute. Thermal conductivity of brass is $110 \mathrm{W}/\mathrm{m}-\mathrm{K}$ and specific latent heat of fusion of ice is $80 \mathrm{cal}/\mathrm{g}$.

A cylinder is made up of two coaxial layers, one of radius $R$ and the other of radius $2R$. The inner and outer portions are respectively made up of substances of thermal conductivities $K$ and $2K$. Determine the effective thermal conductivity between the flat ends of the cylinder.

A cylinder of radius $R$ and length $l$ is made up of a substance whose thermal conductivity $K$ varies with the distance $x$ from the axis as $K=K_{1}x+K_2$. Determine the effective thermal conductivity between the flat faces of the cylinder.