G L Mittal and TARUN MITTAL Solutions for Chapter: Thermal Conduction, Exercise 2: NUMERICALS

The plane surfaces of two sheets of different metals are kept in contact with each other. The thicknesses of sheets are $2.5 cm$ and $3.0 cm$ respectively and the ratio of their thermal conductivities in the same order is $5 : 6$. If the outer surfaces of the sheets are at constant temperatures of $100°C$ and $10°C$ respectively, calculate the temperature of interface.

A composite wall of area $A$ is made of equal thicknesses of lead and iron having thermal conductivities $K$ and $2K$ respectively. The temperatures on the two sides of the composite wall are $100°C$ and $0°C$ with the lead layer on the hotter side. Calculate the steady-state temperature of the lead-iron interface.

Two plates of equal areas are placed in contact with each other. Their thicknesses are $2.0$ and $3.0 cm$ respectively. The temperature of the external surface of the first plate is $-25°C$ and that of the external surface of the second plate is $25°C$. What will be the temperature of the contact-surface, if the plates are of the same material.

Two plates of equal areas are placed in contact with each other. Their thicknesses are $2.0 \mathrm{cm}$ and $3.0 \mathrm{cm}$ respectively. The temperature of the external surface of the first plate is $-25°\mathrm{C}$ and that of the external surface of the second plate is $25°\mathrm{C}$. What will be the temperature of the contact-surface, have thermal conductivities in the ratio $2 : 3$.

An ice box made of $1.75 \mathrm{cm}$ thick wood has on the inner side a $2.0 \mathrm{cm}$ thick layer of cork. If, the temperature of the inner surface of the cork is $0°\mathrm{C}$ and that of the outer surface of wood is $12°\mathrm{C}$, then find the temperature of the interface. Thermal conductivity of wood is $5$ times that of cork.

A square sheet of cork of side $20 \mathrm{cm}$ and thickness $3.0 \mathrm{mm}$ is placed in contact of a square glass sheet of side $20 \mathrm{cm}$ and thickness $5.0 \mathrm{mm}$. The outer faces of this composite sheet are maintained at $100°\mathrm{C}$ and $20°\mathrm{C}$, the cork face being at higher temperature. Find the temperature of the cork-glass interface. The thermal conductivities of cork and glass are $0.063 \mathrm{W} {\mathrm{m}}^{-1}{\mathrm{K}}^{-1}$ and $0.72 \mathrm{W} {\mathrm{m}}^{-1}{\mathrm{K}}^{-1}$ respectively.

A bar of copper of length $0.75 \mathrm{m}$ and a bar of stainless steel of length $1.25 \mathrm{m}$ are joined end to end, each having a cross-sectional area of $101 {\mathrm{m}}^2$. The free ends of the copper and the steel bars are maintained at $100°\mathrm{C}$ and $0°\mathrm{C}$ respectively. Find the temperature of the copper-steel junction.

A bar of copper of length $0.75 m$ and a bar of stainless steel of length $1.25 m$ are joined end to end, each having a cross-sectional area of $101 m^2$. The free ends of the copper and the steel bars are maintained at $100°C$ and $0°C$ respectively. Calculate the rate of heat transmission across the junction. Thermal conductivities of copper and steel are $400$ and $14 J{m}^{-1}{s}^{-1}{K}^{-1}$ respectively.