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 coefficient of thermal conductivity of copper is nine times that of steel. In the composite cylindrical bar shown in the figure. What will be the temperature at the junction of copper and steel ....... $^oC$
The coefficient of thermal conductivity of copper is nine times that of steel. In the composite cylindrical bar shown in the figure. What will be the temperature at the junction of copper and steel ....... $^oC$
Objects $A$ and $B$ that are initially separated from each other and well isolated from their surroundings are then brought into thermal contact. Initially $T_A= 0^oC$ and $T_B = 100^oC$. The specific heat of $A$ is less than the specific heat of $B$. After some time, the system comes to an equilibrium state. The final temperatures are :
Objects $A$ and $B$ that are initially separated from each other and well isolated from their surroundings are then brought into thermal contact. Initially $T_A= 0^oC$ and $T_B = 100^oC$. The specific heat of $A$ is less than the specific heat of $B$. After some time, the system comes to an equilibrium state. The final temperatures are :
Three rods of the same dimensions have thermal conductivities $3k, 2k$ and $k$. They are arranged as shown, with their ends at $100\,^oC, 50\,^oC$ and $0\,^oC$. The temperature of their junction is
Three rods of the same dimensions have thermal conductivities $3k, 2k$ and $k$. They are arranged as shown, with their ends at $100\,^oC, 50\,^oC$ and $0\,^oC$. The temperature of their junction is
Five identical rods are joined as shown in figure. Point $A$ and $C$ are maintained at temperature $120^o C$ and $20^o C$ respectively. The temperature of junction $B$ will be....... $^oC$
Five identical rods are joined as shown in figure. Point $A$ and $C$ are maintained at temperature $120^o C$ and $20^o C$ respectively. The temperature of junction $B$ will be....... $^oC$
At a common temperature, a block of wood and a block of metal feel equally cold or hot. The temperatures of block of wood and block of metal are
At a common temperature, a block of wood and a block of metal feel equally cold or hot. The temperatures of block of wood and block of metal are
- [AIIMS 1999]