A sphere of density rho,specific heat capacit | vedclass

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

Question

(D) According to Newton's Law of Cooling,the rate of heat loss is given by $\frac{dQ}{dt} = \sigma A (T - T_0)$,where $\sigma$ is a constant related t

Vedclass · Accepted Answer

$\frac{1}{r \rho c}$

Vedclass · Answer

(D) According to Newton's Law of Cooling,the rate of heat loss is given by $\frac{dQ}{dt} = \sigma A (T - T_0)$,where $\sigma$ is a constant related to the surface nature,$A$ is the surface area,and $(T - T_0)$ is the temperature difference.Since $dQ = mc \cdot dT$,we have $mc \frac{dT}{dt} = -\sigma A (T - T_0)$.The rate of cooling is $\frac{-dT}{dt} = \frac{\sigma A}{mc} (T - T_0)$.Substituting the values for a sphere: $A = 4 \pi r^2$ and $m = \rho \cdot V = \rho \cdot \frac{4}{3} \pi r^3$.Thus,$\frac{-dT}{dt} = \frac{\sigma (4 \pi r^2)}{\rho (\frac{4}{3} \pi r^3) c} (T - T_0)$.Simplifying this,we get $\frac{-dT}{dt} \propto \frac{1}{\rho r c}$.

Similar Questions

$A$ body cools from $60^{\circ} C$ to $40^{\circ} C$ in $6$ minutes. After the next $6$ minutes,its temperature will be (Temperature of the surroundings is $10^{\circ} C$). (in $^{\circ} C$)

Two circular discs $A$ and $B$ with equal radii are blackened. They are heated to the same temperature and are cooled under identical conditions. What inference do you draw from their cooling curves shown in the figure?

$A$ metallic sphere cools from $50^{\circ}C$ to $40^{\circ}C$ in $300 \, s$. If the atmospheric temperature is $20^{\circ}C$,then the sphere's temperature after the next $5$ minutes will be close to $.....^{\circ}C$.

An ordinary body cools from $4\theta$ to $3\theta$ in $t$ minutes. The temperature of the body after the next $t$ minutes is (Assume Newton's law of cooling and room temperature as $\theta$).

$A$ body cools down from $52.5^{\circ} C$ to $47.5^{\circ} C$ in $5 \ min$ and from $47.5^{\circ} C$ to $42.5^{\circ} C$ in $7.5 \ min$. Then,the temperature of the surroundings is (in $^{\circ} C$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module