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10-2.Transmission of Heat
medium
A beaker full of hot water is kept in a room. If it cools from $80^{\circ} C$ to $75^{\circ} C$ in $t_1$, minutes, from $75^{\circ} C$ to $70^{\circ} C$ in $t_2$ minutes and from $70^{\circ} C$ to $65^{\circ} C$ in $t_3$ minutes, then
A
$t_1=t_2=t_3$
B
$t_1 < t_2=t_3$
C
$t_1 < t_2 < t_3$
D
$t_1>t_2>t_3$
(AIPMT-1995)
Solution
(c) According to Newton's law of cooling
Rate of cooling $\propto$ Mean temperature difference
==> $\frac{{{\rm{Fall in}}\,{\rm{temperature}}}}{{{\rm{Time}}}} \propto \left( {\frac{{{\theta _1} + {\theta _2}}}{2} – {\theta _0}} \right)$
${\left( {\frac{{{\theta _1} + {\theta _2}}}{2}} \right)_1} > {\left( {\frac{{{\theta _1} + {\theta _2}}}{2}} \right)_2} > {\left( {\frac{{{\theta _1} + {\theta _2}}}{2}} \right)_3}$
==> ${T_1} < {T_2} < {T_3}$
Standard 11
Physics
