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10-2.Transmission of Heat
medium
A solid copper cube of edges $1\;cm$ is suspended in an evacuated enclosure. Its temperature is found to fall from ${100^o}C$ to ${99^o}C$ 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 ${100^o}C$ to ${99^o}C$ will be approximately ...... $\sec$
A
$25$
B
$50$
C
$200$
D
$400$
Solution
(c)Rate of cooling $\frac{{\Delta \theta }}{t} = \frac{{A\varepsilon \sigma ({T^4} – T_0^4)}}{{mc}}$
==> $t \propto \frac{m}{A}$
==> $t \propto \frac{m}{A} \propto \frac{{{\rm{Volume}}}}{{{\rm{Area}}}} \propto \frac{{{a^3}}}{{{a^2}}}$
==>$t \propto a$
==> $\frac{{{t_1}}}{{{t_2}}} = \frac{{{a_1}}}{{{a_2}}}$
==> $\frac{{100}}{{{t_2}}} = \frac{1}{2}$ ==>${t_2} = 200sec.$
Standard 11
Physics
