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
Two different rods $A$ and $B$ are kept as shown in figure. The ratio of thermal conductivities of $A$ and $B$ is
Two different rods $A$ and $B$ are kept as shown in figure. The ratio of thermal conductivities of $A$ and $B$ is
A piece of glass is heated to a high temperature and then allowed to cool. If it cracks, a probable reason for this is the following property of glass
A piece of glass is heated to a high temperature and then allowed to cool. If it cracks, a probable reason for this is the following property of glass
Four rods of identical cross-sectional area and made from the same metal form the sides of square. The temperature of two diagonally opposite points and $T$ and $\sqrt 2 $ $T$ respective in the steady state. Assuming that only heat conduction takes place, what will be the temperature difference between other two points
Four rods of identical cross-sectional area and made from the same metal form the sides of square. The temperature of two diagonally opposite points and $T$ and $\sqrt 2 $ $T$ respective in the steady state. Assuming that only heat conduction takes place, what will be the temperature difference between other two points
$Assertion :$ Two thin blankets put together are warmer than a single blanket of double the thickness.
$Reason :$ Thickness increases because of air layer enclosed between the two blankets.
$Assertion :$ Two thin blankets put together are warmer than a single blanket of double the thickness.
$Reason :$ Thickness increases because of air layer enclosed between the two blankets.
- [AIIMS 2010]
A metallic prong consists of $4$ rods made of the same material, cross-sections and same lengths as shown below. The three forked ends are kept at $100^{\circ} C$ and the handle end is at $0^{\circ} C$. The temperature of the junction is ............. $^{\circ} C$
A metallic prong consists of $4$ rods made of the same material, cross-sections and same lengths as shown below. The three forked ends are kept at $100^{\circ} C$ and the handle end is at $0^{\circ} C$. The temperature of the junction is ............. $^{\circ} C$
- [KVPY 2013]