A metre stick has its ends maintained at 100^ ^ ^ C and 0^ ^ ^ C . One end of a rod is kept at 25^ ^ ^ C . At what point on the metre stick should the other end of the rod be touched so that zero heat current flows

Question

Quantrex Academy · Accepted Answer

Correct answer: B. 25 cm from the 0^ ^ ^ C end

In steady state, the temperature gradient along the metre stick is uniform.

Let the

0^{}^{{}^{\circ}} C

end be at

x = 0

and the

100^{}^{{}^{\circ}} C

end be at

x = 100 \text{ cm}

.

The temperature

T

at a distance

x

from the

0^{}^{{}^{\circ}} C

end is given by:

T = 0 + \dfrac{100 - 0}{100} x = x

For zero heat current to flow through the rod, the temperature at the point of contact on the metre stick must be equal to the temperature of the other end of the rod, which is

25^{}^{{}^{\circ}} C

.

Equating the temperatures, we get:

x = 25

Thus, the point of contact should be

25 \text{ cm}

from the

0^{}^{{}^{\circ}} C

end.

A metre stick has its ends maintained at 100^ ^ ^ C and 0^ ^ ^ C ....

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