Question

two solid spheres A and B made of the same material have radii rA and rB respectively.both the spheres are cooled from the same temperature under the conditions valid for Newton's law of cooling.the ratio of the rate of change of temperature in A and B is​

Answer 1

Given that,

Radius of solid A $r=r_{A}$

Radius of solid B $r=r_{B}$

According to question,

Both the spheres are cooled from the same temperature.

We know that,

The newton's law of cooling is defined as,

$\dfrac{dT}{dt}=-k(T-T_{a})$

Where, T = temperature of material

$T_{a}$ = ambient temperature

We need to calculate the ratio of the rate of change of temperature in A and B

Using newton's law of cooling

$\dfrac{\dfrac{dT_{A}}{dt}}{\dfrac{dT_{B}}{dt}}=\dfrac{-k(T_{A}-T_{a_{A}})}{-k(T_{B}-T_{a_{B}})}$

Here, $T_{A}=T_{B}$

$\dfrac{dT_{a}}{dT_{b}}=\dfrac{T_{a_{A}}}{T_{a_{B}}}$

Hence, The ratio of the rate of change of temperature in A and B is $\dfrac{T_{a_{A}}}{T_{a_{B}}}$