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Question
The ends of a metre stick are maintained at 100°C and 0°C. One end of a rod is maintained at 25°C. Where should its other end be touched on the metre stick so that there is no heat current in the rod in steady state?
Solution
One end of the rod is at a temperature of 25°C. So, if no heat current flows through the rod in steady state, then the other end of the rod should also be at a temperature of 25°C.
Let the point at which the other end of the rod is touched be C.
No heat flows through the rod when the temperature at point C is also 25°C.
Heat current through AC = Heat current through CB
⇒ `(DeltaT)_"AC"/(x/"KA") = (DeltaT)_(CB)/(100-x/(KA))`
⇒ `((100 - 25))/x = (25 - 0)/(100-x)`
⇒`3/x = 1/(100-x)`
⇒ 300 - 3x = x
⇒ 300 = 4x
x = 75 cm
Thus, it should be touched at 75 cm from 100°C end.
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