Heat Transfer

In summer water kept in a bottle become hot but when cover the bottle with a wet towel the water becomes cool. Why?

Two rods, one made of copper and the other made of steel of same length and same cross-sectional area are joined together. The thermal conductivity of copper and steel are $385 \mathrm{J} {\mathrm{s}}^{–1} {\mathrm{K}}^{–1} {\mathrm{m}}^{–1}$ and $50 \mathrm{J} {\mathrm{s}}^{–1} {\mathrm{K}}^{–1} {\mathrm{m}}^{–1}$ respectively. The free ends of copper and steel are held at $100° \mathrm{C}$ and $0° \mathrm{C}$ respectively. Calculate the temperature at the junction.

When $150 \mathrm{g}$ of ice at $0°\mathrm{C}$ is mixed with $300 \mathrm{g}$ of water at$50°\mathrm{C}$ in a container, the resulting temperature is

$L_f=3.34\times {10}^5 \mathrm{J} {\mathrm{kg}}^{-1}, {\mathrm{S}}_{\mathrm{w}}=4186 \mathrm{J} {\mathrm{Kg}}^{-1} {\mathrm{K}}^{-1}$

A solid iron sphere and a hollow iron sphere, both have the same mass and are at the same temperature. When placed in a colder surrounding, the heat loss per unit time will be 

A metal vessel of negligible heat capacity contains$0.5 \mathrm{kg}$ of water (of specific heat capacity $4200 \mathrm{J} {\mathrm{kg}}^{-1}{\mathrm{K}}^{-1}$). It is heated from $15°\mathrm{C}$to $85°\mathrm{C}$ by $750 \mathrm{W}$ immersion heater in$4 \mathrm{minutes}$. The average loss of heat in watts to the surroundings from the vessel during this time is nearly: 

Why is the mode of heat transfer in Mercury is by conduction although it is a liquid?

Two metallic blocks $M_1$ and $M_2$ of same area of cross-section are connected to each other (as shown in figure). If the thermal conductivity of $M_2$ is $K$ then the thermal conductivity of $M_1$ will be : [Assume steady state heat conduction]

Four semicircular rod of cross section area $A$, radius $r$, thermal conductivity '$K$' are connected as shown then thermal resistance of configuration across point $A$ and $B$ is:

Is steel is a good conductor of heat?

A composite cylinder is made by two materials having thermal conductivities $k_1$ and $k_2$ as shown. Temperature of the two flat faces of cylinder are maintained at $T_1$ and $T_{2.}$

The end $A$ of a rod $AB$ of length $1 \mathrm{m}$ is maintained at $100 °\mathrm{C}$ and the end $B$at $10 °\mathrm{C}$. What is the temperature (in $°\mathrm{C}$) at a distance of $60 \mathrm{cm}$ from the end $B$?

A room has a $4 \mathrm{m}\times 4 \mathrm{m}\times 10 \mathrm{cm}$ concrete roof $\left(k=1.26 \mathrm{w} {\mathrm{m}}^{-1}-{}^{\circ }\mathrm{C}\right)$. At some instant, the temperature outside is $46 °\mathrm{C}$ and that inside is $32 °\mathrm{C}$. If the bricks $\left(k=0.65 \mathrm{w} {\mathrm{m}}^{-1}-{}^{\circ }\mathrm{C}\right)$ of thickness $7.5 \mathrm{cm}$ are laid down on the roof. Calculate the rate of heat flow under the same temperature condition (neglect convection).

A composite spherical shell is made up of two materials having thermal conductivities $K$ and$2K$  respectively as shown in the figure. The temperature at the inner most surface is maintained at $T$ whereas the temperature at the outer most surface is maintained at $10 \mathrm{T}.\mathrm{A},\mathrm{B},\mathrm{C}$ and $\mathrm{D}$ are four points in the outer material such that $\mathrm{AB}=$ $\mathrm{BC}=\mathrm{CD}$. The net rate of heat flow from the outermost surface to the innermost surface of the shell will be (Neglect any radiation)

Many species cool themselves by sweating, because as the sweat evaporates, heat is given to the surroundings. A person exercising strenuously has an evaporative heat loss rate of about $290 \mathrm{W}$. If this person exercises strenuously for $14 \min$, how much water (in gm) must he drink to replenish his fluid loss? The heat of vaporization of water is $580 \mathrm{cal} {\mathrm{g}}^{-1}$ at normal skin temperature. (Take: $1 \mathrm{cal} = 4.2 \mathrm{J}$ )

Inner surface of a cylindrical shell of length $\ell$ and of material of thermal conductivity $k$ is kept at constant temperature $T_1$ and the outer surface of the cylinder is kept at constant temperature $T_2$ such that $\left(T_1>T_2\right)$ as shown in figure. Heat flows from inner surface to outer surface to outer surface radially outward. Inner and outer radii of the shell are $R$ and $2R$ respectively. Due to lack of space this cylinder has to be replaced by a smaller cylinder of length $\frac{\ell }{2}$ inner and outer radii $\frac{R}{8}$ and $R$ respectively and thermal conductivity of material $nk$. If rate of radially outward heat flow remains same for same temperature of inner and outer surface i.e. $T_1$ and $T_2$, then find the value of $n$.

List the applications of thermal conductivity.

What are the applications of thermal convection?

Two different materials $M_1,M_2$ of equal dimensions (length $L$ and uniform cross-sectional area $A$) having thermal conductivities $k_1$ and $k_2$ respectively are connected together through a bolt $M_3$. The bolt (length $=2 L$, area $=A/n$) is of another material with thermal conductivity $k_3$ such that $n\gg 1$. The left sides of the material $M_1$ and $M_3$ are kept at the temperature $T_1$ whereas the right sides of the material $M_2$ and $M_3$ are kept at the temperature $T_2$ as shown in the figure below such that $T_1>T_2$. Assume that the bolt $\left(M_3\right)$ is thermally insulated from materials $M_1$ and $M_2$. The equivalent thermal resistance of this system is

Explain the cooling of Transformer based on thermal convection.

Explain thermal convection along with the applications of convection in daily life.