Two thin metallic spherical shells of radii ${r}_{1}$ and ${r}_{2}$ $\left({r}_{1}<{r}_{2}\right)$ are placed with their centres coinciding. A material of thermal conductivity ${K}$ is filled in the space between the shells. The inner shell is maintained at temperature $\theta_{1}$ and the outer shell at temperature $\theta_{2}\left(\theta_{1}<\theta_{2}\right)$. The rate at which heat flows radially through the material is :-
Two thin metallic spherical shells of radii ${r}_{1}$ and ${r}_{2}$ $\left({r}_{1}<{r}_{2}\right)$ are placed with their centres coinciding. A material of thermal conductivity ${K}$ is filled in the space between the shells. The inner shell is maintained at temperature $\theta_{1}$ and the outer shell at temperature $\theta_{2}\left(\theta_{1}<\theta_{2}\right)$. The rate at which heat flows radially through the material is :-
- [JEE MAIN 2021]
- A
$\frac{4 \pi {Kr}_{1} {r}_{2}\left(\theta_{2}-\theta_{1}\right)}{{r}_{2}-{r}_{1}}$
- B
$\frac{\pi{r}_{1} {r}_{2}\left(\theta_{2}-\theta_{1}\right)}{{r}_{2}-{r}_{1}}$
- C
$\frac{{K}\left(\theta_{2}-\theta_{1}\right)}{{r}_{2}-{r}_{1}}$
- D
$\frac{{K}\left(\theta_{2}-\theta_{1}\right)\left({r}_{2}-{r}_{1}\right)}{4 \pi {r}_{1} {r}_{2}}$
Similar Questions
The two opposite faces of a cubical piece of iron (thermal conductivity $= 0.2\, CGS$ units) are at ${100^o}C$ and ${0^o}C$ in ice. If the area of a surface is $4c{m^2}$, then the mass of ice melted in $10$ minutes will be ...... $gm$
The two opposite faces of a cubical piece of iron (thermal conductivity $= 0.2\, CGS$ units) are at ${100^o}C$ and ${0^o}C$ in ice. If the area of a surface is $4c{m^2}$, then the mass of ice melted in $10$ minutes will be ...... $gm$
The heat is flowing through a rod of length $50 cm$ and area of cross-section $5c{m^2}$. Its ends are respectively at ${25^o}C$ and ${125^o}C$. The coefficient of thermal conductivity of the material of the rod is $0.092 kcal/m×s×^\circ C$. The temperature gradient in the rod is
The heat is flowing through a rod of length $50 cm$ and area of cross-section $5c{m^2}$. Its ends are respectively at ${25^o}C$ and ${125^o}C$. The coefficient of thermal conductivity of the material of the rod is $0.092 kcal/m×s×^\circ C$. The temperature gradient in the rod is
The three rods shown in figure have identical dimensions. Heat flows from the hot end at a rate of $40 \,W$ in the arrangement $(a)$. Find the rates of heat flow when the rods are joined as in arrangement $(b)$ is ......... $W$ (Assume $K_al=200 \,W / m ^{\circ} C$ and $\left.K_{c u}=400 \,W / m ^{\circ} C \right)$
The three rods shown in figure have identical dimensions. Heat flows from the hot end at a rate of $40 \,W$ in the arrangement $(a)$. Find the rates of heat flow when the rods are joined as in arrangement $(b)$ is ......... $W$ (Assume $K_al=200 \,W / m ^{\circ} C$ and $\left.K_{c u}=400 \,W / m ^{\circ} C \right)$
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
Three identical rods have been joined at a junction to make it a $Y$ shape structure. If two free ends are maintained at $90\,^oC$ and the third end is at $30\,^oC$ , then what is the junction temperature $\theta $ ?......... $^oC$
Three identical rods have been joined at a junction to make it a $Y$ shape structure. If two free ends are maintained at $90\,^oC$ and the third end is at $30\,^oC$ , then what is the junction temperature $\theta $ ?......... $^oC$