Two walls of thicknesses $d_1$ and $d_2$ and thermal conductivities $k_1$ and $k_2$ are in contact. In the steady state, if the temperatures at the outer surfaces are ${T_1}$ and ${T_2}$, the temperature at the common wall is
Two walls of thicknesses $d_1$ and $d_2$ and thermal conductivities $k_1$ and $k_2$ are in contact. In the steady state, if the temperatures at the outer surfaces are ${T_1}$ and ${T_2}$, the temperature at the common wall is
- A
$\frac{{{k_1}{T_1}{d_2} + {k_2}{T_2}{d_1}}}{{{k_1}{d_2} + {k_2}{d_1}}}$
- B
$\frac{{{k_1}{T_1} + {k_2}{d_2}}}{{{d_1} + {d_2}}}$
- C
$\left( {\frac{{{k_1}{d_1} + {k_2}{d_2}}}{{{T_1} + {T_2}}}} \right){T_1}{T_2}$
- D
$\frac{{{k_1}{d_1}{T_1} + {k_2}{d_2}{T_2}}}{{{k_1}{d_1} + {k_2}{d_2}}}$
Similar Questions
There is formation of layer of snow $x\,cm$ thick on water, when the temperature of air is $ - {\theta ^o}C$ (less than freezing point). The thickness of layer increases from $x$ to $y$ in the time $t$, then the value of $t$is given by
There is formation of layer of snow $x\,cm$ thick on water, when the temperature of air is $ - {\theta ^o}C$ (less than freezing point). The thickness of layer increases from $x$ to $y$ in the time $t$, then the value of $t$is given by
A rod $C D$ of thermal resistance $10.0\; {KW}^{-1}$ is joined at the middle of an identical rod ${AB}$ as shown in figure, The end $A, B$ and $D$ are maintained at $200^{\circ} {C}, 100^{\circ} {C}$ and $125^{\circ} {C}$ respectively. The heat current in ${CD}$ is ${P}$ watt. The value of ${P}$ is ... .
A rod $C D$ of thermal resistance $10.0\; {KW}^{-1}$ is joined at the middle of an identical rod ${AB}$ as shown in figure, The end $A, B$ and $D$ are maintained at $200^{\circ} {C}, 100^{\circ} {C}$ and $125^{\circ} {C}$ respectively. The heat current in ${CD}$ is ${P}$ watt. The value of ${P}$ is ... .
- [JEE MAIN 2021]
A metal rod of length $2\, m$ has cross-sectional areas $2A$ and $A$ as shown in the following figure. The two ends are maintained at temperatures $100\,^oC$ and $70\,^oC$. The temperature of middle point $C$ is ........ $^oC$
A metal rod of length $2\, m$ has cross-sectional areas $2A$ and $A$ as shown in the following figure. The two ends are maintained at temperatures $100\,^oC$ and $70\,^oC$. The temperature of middle point $C$ is ........ $^oC$
The two ends of a metal rod are maintained at temperatures $100 ^o C$ and $110^o C$. The rate of heat flow in the rod is found to be $4.0\ J/s$. If the ends are maintained at temperatures $200^o\ C$ and $210^o\ C$, the rate of heat flow will be.... $J/s$
The two ends of a metal rod are maintained at temperatures $100 ^o C$ and $110^o C$. The rate of heat flow in the rod is found to be $4.0\ J/s$. If the ends are maintained at temperatures $200^o\ C$ and $210^o\ C$, the rate of heat flow will be.... $J/s$
- [AIPMT 2015]
The thickness of a metallic plate is $0.4 cm$ . The temperature between its two surfaces is ${20^o}C$. The quantity of heat flowing per second is $50$ calories from $5c{m^2}$ area. In $CGS$ system, the coefficient of thermal conductivity will be
The thickness of a metallic plate is $0.4 cm$ . The temperature between its two surfaces is ${20^o}C$. The quantity of heat flowing per second is $50$ calories from $5c{m^2}$ area. In $CGS$ system, the coefficient of thermal conductivity will be