Liquid is filled in a vessel which is kept in a room with temperature ${20^o}C$. When the temperature of the liquid is ${80^o}C$, then it loses heat at the rate of $60\;cal/\sec $. What will be the rate of loss of heat when the temperature of the liquid is ${40^o}C$ ....... $cal/\sec $
Medium
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(d) Rate of loss of heat $\left( {\frac{{\Delta Q}}{t}} \right) \propto \,$temperature difference $\Delta \theta$
$\frac{{{{\left( {\frac{{\Delta Q}}{t}} \right)}_1}}}{{{{\left( {\frac{{\Delta Q}}{t}} \right)}_2}}} = \frac{{\Delta {\theta _2}}}{{\Delta {\theta _1}}}$
$\frac{{{{\left( {\frac{{\Delta Q}}{t}} \right)}_1}}}{{{{\left( {\frac{{\Delta Q}}{t}} \right)}_2}}} = \frac{{\Delta {\theta _2}}}{{\Delta {\theta _1}}}$
==> $\frac{{60}}{{{{\left( {\frac{{\Delta Q}}{t}} \right)}_2}}} = \frac{{80 - 20}}{{40 - 20}}$
==> ${\left( {\frac{{\Delta Q}}{t}} \right)_2} = \frac{{20\,cal}}{{sec}}$
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