The two ends of a metal rod are maintained at temperatures $100 ^o C$ and $110^o C$. The rate of heat flow in the rod is found to be $4.0\ J/s$. If the ends are maintained at temperatures $200^o\ C$ and $210^o\ C$, the rate of heat flow will be.... $J/s$
AIPMT 2015, Medium
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We know that the rate of flow of heat is proportional to temperature difference between two ends. So
$\frac{{dQ}}{{dt}} \propto \left( {{T_2} - {T_1}} \right)$
$\frac{{dQ}}{{dt}} = k\left( {{T_2} - {T_1}} \right)$
$\frac{{d{Q_1}}}{{dt}} = k\left[ {110 - 100} \right] = k \times 10$
$\frac{{d{Q_2}}}{{dt}} = k \times 10$
$\frac{{d{Q_1}}}{{dt}} = \frac{{d{Q_2}}}{{dt}} = 4.0\,\,J/s$
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