A solid copper cube of edges 1 ;cm is suspended in an evacuated e… - Vidyadip

MCQ

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
$50$
✓
$200$
D
$400$

✓

Answer

Correct option: C.

$200$

c
(c)Rate of cooling $\frac{{\Delta \theta }}{t} = \frac{{A\varepsilon \sigma ({T^4} - T_0^4)}}{{mc}}$

==> $t \propto \frac{m}{A}$

==> $t \propto \frac{m}{A} \propto \frac{{{\rm{Volume}}}}{{{\rm{Area}}}} \propto \frac{{{a^3}}}{{{a^2}}}$

==>$t \propto a$

==> $\frac{{{t_1}}}{{{t_2}}} = \frac{{{a_1}}}{{{a_2}}}$

==> $\frac{{100}}{{{t_2}}} = \frac{1}{2}$ ==>${t_2} = 200sec.$

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