A brass boiler has a base area of $0.15\; m ^{2}$ and thickness $1.0\; cm .$ It boils water at the rate of $6.0\; kg / min$ when placed on a gas stove. Estimate the temperature (in $^oC$) of the part of the flame in contact with the boiler. Thermal conductivity of brass $=109 \;J s ^{-1} m ^{-1} K ^{-1} ;$ Heat of vaporisation of water $=2256 \times 10^{3}\; J kg ^{-1}$
Thickness of the boiler, $l=1.0 cm =0.01 m$
Boiling rate of water, $R=6.0 kg / min$
Mass, $m=6 kg$
Time, $t=1 \min =60 s$
Thermal conductivity of brass, $K=109 Js ^{-1} m ^{-1} K ^{-1}$
Heat of vaporisation, $L=2256 \times 10^{3} J kg ^{-1}$
The amount of heat flowing into water through the brass base of the boiler is given by
$\theta=\frac{K A\left(T_{1}-T_{2}\right) t}{l}\dots (i)$
Where,
$T_{1}=$ Temperature of the flame in contact with the boiler
$T_{2}=$ Boiling point of water $=100^{\circ} C$
Heat required for boiling the water
$\theta=m L \ldots(i i)$
Equating equations $(i)$ and $(i i),$ we get:
$\therefore m L=\frac{K A\left(T_{1}-T_{2}\right) t}{l}$
$T_{1}-T_{2}=\frac{m L l}{K A t}$
$=\frac{6 \times 2256 \times 10^{3} \times 0.01}{109 \times 0.15 \times 60}$
$=137.98^{\circ} C$
Therefore, the temperature of the part of the flame in contact with the boiler is $237.98\,^{\circ} C$
If the radius and length of a copper rod are both doubled, the rate of flow of heat along the rod increases ....... times
Three rods of Copper, Brass and Steel are welded together to form a $Y$ shaped structure. Area of cross - section of each rod $= 4\ cm^2$ . End of copper rod is maintained at $100^o C $ where as ends ofbrass and steel are kept at $0^o C$. Lengths of the copper, brass and steel rods are $46, 13$ and $12\ cms$ respectively. The rods are thermally insulated from surroundings excepts at ends. Thermal conductivities of copper, brass and steel are $0.92, 0.26$ and $0.12\ CGS$ units respectively. Rate ofheat flow through copper rod is ....... $cal\, s^{-1}$
A rod of length $L$ with sides fully insulated is of a material whose thermal conductivity varies with $\alpha$ temperature as $ K= \frac{\alpha }{T}$, where $\alpha$ is a constant. The ends of the rod are kept at temperature $T_1$ and $T_2$. The temperature $T$ at $x,$ where $x$ is the distance from the end whose temperature is $T_1$ is
Value of temperature gradient is $80\,^oC/m$ on a rod of $0.5\,m$ length. Temperature of hot end is $30\,^oC$, then what is the temperature of cold end ?
If the ratio of coefficient of thermal conductivity of silver and copper is $10 : 9$ , then the ratio of the lengths upto which wax will melt in Ingen Hausz experiment will be