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प्रश्न
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?
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उत्तर
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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