A solid copper sphere (density $\rho $ and specific heat capacity $c$ ) of radius $r$ at an initial temperature $200K$ is suspended inside a chamber whose walls are at almost $0K$ . The time required (in $\mu s$) for the temperature of the sphere to drop to $100\, K$ is
A solid copper sphere (density $\rho $ and specific heat capacity $c$ ) of radius $r$ at an initial temperature $200K$ is suspended inside a chamber whose walls are at almost $0K$ . The time required (in $\mu s$) for the temperature of the sphere to drop to $100\, K$ is
- [IIT 1991]
- A
$\frac{{72}}{7}\frac{{r\rho c}}{\sigma }$
- B
$\frac{7}{{72}}\frac{{r\rho c}}{\sigma }$
- C
$\frac{{27}}{7}\frac{{r\rho c}}{\sigma }$
- D
$\frac{7}{{27}}\frac{{r\rho c}}{\sigma }$
Similar Questions
A body takes $4\, {min}$. to cool from $61^{\circ} {C}$ to $59^{\circ} {C}$. If the temperature of the surroundings is $30^{\circ} {C}$, the time taken by the body to cool from $51^{\circ} {C}$ to $49^{\circ} {C}$ is $....\,min$
A body takes $4\, {min}$. to cool from $61^{\circ} {C}$ to $59^{\circ} {C}$. If the temperature of the surroundings is $30^{\circ} {C}$, the time taken by the body to cool from $51^{\circ} {C}$ to $49^{\circ} {C}$ is $....\,min$
- [JEE MAIN 2021]
A body takes $5$ minutes to cool from $90^oC$ to $60^oC$. If the temperature of the surroundings is $20^oC$, the time taken by it to cool from $60^oC$ to $30^oC$ will be ...... $\min.$
A body takes $5$ minutes to cool from $90^oC$ to $60^oC$. If the temperature of the surroundings is $20^oC$, the time taken by it to cool from $60^oC$ to $30^oC$ will be ...... $\min.$
If a piece of metal is heated to temperature $\theta$ and then allowed to cool in a room which is at temperature $\theta_0$, the graph between the temperature $T$ of the metal and time t will be closest to
If a piece of metal is heated to temperature $\theta$ and then allowed to cool in a room which is at temperature $\theta_0$, the graph between the temperature $T$ of the metal and time t will be closest to
- [JEE MAIN 2013]
A hot metallic sphere of radius $r$ radiates heat. It's rate of cooling is
A hot metallic sphere of radius $r$ radiates heat. It's rate of cooling is
A sphere at temperature $600\,K$ is placed in an environment of temperature is $200\,K$ . Its cooling rate is $H$ . If its temperature reduced to $400\,K$ then cooling rate in same environment will become
A sphere at temperature $600\,K$ is placed in an environment of temperature is $200\,K$ . Its cooling rate is $H$ . If its temperature reduced to $400\,K$ then cooling rate in same environment will become