(C) The rate of cooling is given by $\frac{d\theta}{dt} = \frac{A \epsilon \sigma (T^4 - T_0^4)}{mc}$.Since the temperature change $\Delta \theta$ is

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(C) The rate of cooling is given by $\frac{d\theta}{dt} = \frac{A \epsilon \sigma (T^4 - T_0^4)}{mc}$.Since the temperature change $\Delta \theta$ is small,we can write $\frac{\Delta \theta}{t} \propto \frac{A}{mc}$.Here,$m = \rho V = \rho a^3$ and $A = 6a^2$,where $a$ is the edge length.Thus,$t \propto \frac{mc}{A} \propto \frac{\rho a^3 c}{6a^2} \propto a$.Therefore,$\frac{t_1}{t_2} = \frac{a_1}{a_2}$.Given $t_1 = 100\;s$,$a_1 = 1\;cm$,and $a_2 = 2\;cm$.$\frac{100}{t_2} = \frac{1}{2} \implies t_2 = 200\;s$.

Class 11 Physics 2 Thermal Properties of Matter: Heat Transfer Newton's Law of Cooling

Medium

$A$ solid copper cube of edges $1\;cm$ is suspended in an evacuated enclosure. Its temperature is found to fall from $100^{\circ}C$ to $99^{\circ}C$ in $100\;s$. Another solid copper cube of edges $2\;cm$,with similar surface nature,is suspended in a similar manner. The time required for this cube to cool from $100^{\circ}C$ to $99^{\circ}C$ will be approximately ...... $s$.

A
$25$
B
$50$
C
$200$
D
$400$

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Class 11

Physics Questions

Chapter

2 Thermal Properties of Matter: Heat Transfer

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Newton's Law of Cooling

$A$ hot body,obeying Newton's law of cooling,is cooling down from its peak value $80\,^oC$ to an ambient temperature of $30\,^oC$. It takes $5\,minutes$ to cool down from $80\,^oC$ to $40\,^oC$. How many minutes will it take to cool down from $62\,^oC$ to $32\,^oC$? (Given $\ln 2 = 0.693, \ln 5 = 1.609$)

DifficultJEE MAIN 2014

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If a liquid cools from $95^{\circ}C$ to $90^{\circ}C$ in $30 \, s$ and from $55^{\circ}C$ to $50^{\circ}C$ in $70 \, s$,then the temperature of the surroundings is ...... $^{\circ}C$. (in $.5$)

Difficult

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$A$ block of metal is heated to a temperature much higher than the room temperature and allowed to cool in a room free from air currents. Which of the following curves correctly represents the rate of cooling?

Medium

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The rate of cooling at $600 \ K$ is $R$,given the surrounding temperature is $300 \ K$. What is the rate of cooling at $900 \ K$?

Medium

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$A$ body cools in $7$ minutes from $60^\circ C$ to $40^\circ C$. What time (in minutes) does it take to cool from $40^\circ C$ to $28^\circ C$, if its surrounding temperature is $10^\circ C$? (Newton's law of cooling holds good)

DifficultMHT CET 2026

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If a liquid cools from $95^{\circ}C$ to $90^{\circ}C$ in $30 \, s$ and from $55^{\circ}C$ to $50^{\circ}C$ in $70 \, s$,then the temperature of the surroundings is ...... $^{\circ}C$. (in $.5$)

$A$ block of metal is heated to a temperature much higher than the room temperature and allowed to cool in a room free from air currents. Which of the following curves correctly represents the rate of cooling?

The rate of cooling at $600 \ K$ is $R$,given the surrounding temperature is $300 \ K$. What is the rate of cooling at $900 \ K$?

$A$ body cools in $7$ minutes from $60^\circ C$ to $40^\circ C$. What time (in minutes) does it take to cool from $40^\circ C$ to $28^\circ C$, if its surrounding temperature is $10^\circ C$? (Newton's law of cooling holds good)

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