Four spheres A, B, C and D are of the same ra | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) The rate of cooling $R_F = \frac{d	heta}{dt}$ is given by Newton's Law of Cooling as $R_F \propto \frac{1}{ms}$,where $m$ is the mass and $s$ is

Vedclass · Accepted Answer

$D$

Vedclass · Answer

(C) The rate of cooling $R_F = \frac{d	heta}{dt}$ is given by Newton's Law of Cooling as $R_F \propto \frac{1}{ms}$,where $m$ is the mass and $s$ is the specific heat capacity.Since the spheres have the same radius,their volumes $V$ are equal. Mass $m = ho V$,where $ho$ is the density.Thus,$R_F \propto \frac{1}{(ho V)s} \propto \frac{1}{ho s}$.We need to calculate the product $ho s$ for each sphere:For $A$: $ho s = 6 	imes 2 = 12$For $B$: $ho s = 3 	imes 5 = 15$For $C$: $ho s = 4 	imes 4 = 16$For $D$: $ho s = 5 	imes 6 = 30$The rate of cooling is slowest when the product $ho s$ is maximum.Comparing the values $12, 15, 16, 30$,the maximum value is $30$,which corresponds to sphere $D$.

Similar Questions

Two metal spheres,one solid and one hollow,are heated to $300^{\circ}C$ and allowed to cool in the same environment. The rate of heat loss will be:

$A$ black body calorimeter filled with hot water cools from $60^{\circ}C$ to $50^{\circ}C$ in $4 \text{ min}$ and from $40^{\circ}C$ to $30^{\circ}C$ in $8 \text{ min}$. The approximate temperature of the surrounding is ........ $^{\circ}C$.

Hot water kept in a beaker placed in a room cools from $70^{\circ}C$ to $60^{\circ}C$ in $4$ minutes. The time taken by it to cool from $69^{\circ}C$ to $59^{\circ}C$ will be

$A$ body takes $10$ minutes to cool down from $62^{\circ}C$ to $50^{\circ}C$. If the temperature of the surrounding is $26^{\circ}C$,then in the next $10$ minutes,the temperature of the body will be ......... $^{\circ}C$.

$A$ cup of tea cools from $65.5 ^\circ C$ to $62.5 ^\circ C$ in $1$ minute in a room at $22.5 ^\circ C$. How long will the same cup of tea take,in minutes,to cool from $46.5 ^\circ C$ to $40.5 ^\circ C$ in the same room? (Choose the nearest value)

Vedclass Test Series

Exam Paper Generator

Online Exam Module