Question

The two ends of a metal rod are maintained at temperatures $100^{\circ} C$ and $110^{\circ} C$. The rate of heat flow in the rod is found to be $4\, Js ^{-1}$. If the ends are maintained at temperatures $200^{\circ} C$ and $210^{\circ} C$, the rate of heat flow will be

• A. $44.0\, Js ^{-1}$
• B. $16.8\, Js ^{-1}$
• C. $8.0\, Js ^{-1}$
• D. $4.0 \,Js ^{-1}$

Answer 1

Answer: (D)

The two ends of a rod are maintained at temperatures $100^{\circ} C$ and $110^{\circ} C$.
Given, $\Delta T_{1}=110^{\circ} C -100^{\circ} C =10^{\circ} C$
$\frac{d Q_{1}}{d t}=4 \,Js ^{-1}$
$\Delta T_{2}=210-200=10^{\circ} C$
$\frac{d Q_{2}}{d t}=?$
As the rate of heat flow is directly proportional to the temperature difference and the temperature difference in both cases is same, i.e. $10^{\circ} C$.
So, the same rate of heat will flow in the second case.
Hence, $ \frac{d Q_{2}}{d t}=4 \,Js ^{-1}$
So, if the ends of the rod are maintained at temperatures $200^{\circ} C$ and $210^{\circ} C$, then the rate of heat flow will remain same,
i.e. $4 \,Js ^{-1}$.