(C) According to Stefan's Law,the rate of cooling (rate of fall of temperature) is given by $\frac{d\theta}{dt} = \frac{\sigma A (T^4 - T_0^4)}{MS}$.S

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$\frac{R_2 \rho_2 S_2}{R_1 \rho_1 S_1}$

(C) According to Stefan's Law,the rate of cooling (rate of fall of temperature) is given by $\frac{d\theta}{dt} = \frac{\sigma A (T^4 - T_0^4)}{MS}$.Since $M = V \rho = \frac{4}{3} \pi R^3 \rho$ and $A = 4 \pi R^2$,we have $\frac{d\theta}{dt} \propto \frac{A}{MS} = \frac{4 \pi R^2}{(\frac{4}{3} \pi R^3 \rho) S} = \frac{3}{R \rho S}$.Therefore,the ratio of the rates of cooling is $\frac{(d\theta/dt)_1}{(d\theta/dt)_2} = \frac{R_2 \rho_2 S_2}{R_1 \rho_1 S_1}$.

Class 11 Physics 10-2.Heat Transfer Newton's Law of Cooling

Medium

Two spheres of radii $R_1$ and $R_2$ have densities $\rho_1$ and $\rho_2$ and specific heats $S_1$ and $S_2$. If they are heated to the same temperature,what is the ratio of their rates of cooling?

A
$\frac{R_2}{R_1}$
B
$\frac{R_1 \rho_2 S_2}{R_2 \rho_1 S_1}$
C
$\frac{R_2 \rho_2 S_2}{R_1 \rho_1 S_1}$
D
$\left( \frac{R_1}{R_2} \right)^2$

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10-2.Heat Transfer

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Newton's Law of Cooling

It takes $1 \, min$ for hot water to cool from $80^{\circ}C$ to $60^{\circ}C$. Find the time taken (in $sec$) to cool from $60^{\circ}C$ to $50^{\circ}C$. The temperature of the surroundings is $30^{\circ}C$.

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For a small temperature difference between the body and the surroundings,the relation between the rate of loss of heat $R$ and the temperature of the body $\theta$ is depicted by:

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Water and turpentine oil (specific heat less than that of water) are both heated to the same temperature. Equal amounts of these,placed in identical calorimeters,are then left to cool in the air. Which of the following statements is correct regarding their cooling curves?

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In an experiment to verify Newton's law of cooling,a graph is plotted between the temperature difference $(\Delta T)$ of the water and surroundings and time as shown in the figure. The initial temperature of water is taken as $80^{\circ}C$. The value of $t_{2}$ as mentioned in the graph will be...........

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$A$ metal sphere cools at the rate of $1.5^{\circ} C / min$ when its temperature is $80^{\circ} C$. At what rate will it cool when its temperature falls to $50^{\circ} C$? [Temperature of surrounding is $30^{\circ} C$]

MediumMHT CET 2021

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Two spheres of radii $R_1$ and $R_2$ have densities $\rho_1$ and $\rho_2$ and specific heats $S_1$ and $S_2$. If they are heated to the same temperature,what is the ratio of their rates of cooling?

Similar Questions

It takes $1 \, min$ for hot water to cool from $80^{\circ}C$ to $60^{\circ}C$. Find the time taken (in $sec$) to cool from $60^{\circ}C$ to $50^{\circ}C$. The temperature of the surroundings is $30^{\circ}C$.

For a small temperature difference between the body and the surroundings,the relation between the rate of loss of heat $R$ and the temperature of the body $\theta$ is depicted by:

Water and turpentine oil (specific heat less than that of water) are both heated to the same temperature. Equal amounts of these,placed in identical calorimeters,are then left to cool in the air. Which of the following statements is correct regarding their cooling curves?

$A$ metal sphere cools at the rate of $1.5^{\circ} C / min$ when its temperature is $80^{\circ} C$. At what rate will it cool when its temperature falls to $50^{\circ} C$? [Temperature of surrounding is $30^{\circ} C$]

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