Question

A sphere of density $d$, specific heat capacity $c$ and radius $r$ is hung by a thermally insulating thread in an enclosure which is kept at lower temperature than the sphere. The temperature of the sphere starts to drop at a rate which is proportional to :

• A. $c/r^{3}d$
• B. $1/r^{3}dc$
• C. $3r^{3}dc$
• D. $1/rdc$

Answer 1

Answer: (D)

$1/rdc$

The loss of heat per unit area id given by

$-mc\frac{dT}{dt}\propto Temperaturedifference$

$-\frac{-4\pi r^3}{3}dc\frac{dT}{dt}=K\left(\Delta T\right).\left(4\pi r^2\right)$

Now, rate of fall of temperature is given by

$\frac{-dT}{dt}\propto \frac{1}{rdc}$