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?

Answer 1

Answer:

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Explanation:

Let the point to be touched be ‘B’ No heat will flow when, the temp at that point is also 25°C i.e. QAB = QBC So, (KA(100 - 25)/(100 - x) = (KA(25 - 0)/x => 75x = 2500 – 25x => 100x = 2500 => x = 25cm from the end with 0°CRead more on Sarthaks.com - https://www.sarthaks.com/63502/the-ends-of-metre-stick-are-maintained-at-100c-and-0c-one-end-of-a-rod-is-maintained-at-25c

Answer 2

Other end is needed to be touched at 0.75 m

Explanation:

The temperature difference between the ends of the meter stick AB:

ΔT = $T_2-T_1$= 100-0 = 100°C

The temperature of one end of the rod: $T_3$ = 25 °C

Length of the rod: l = 1 m

Here, C is the point at which the other end of the rod is placed. Distance between A and C = x Distance between C and B = 1- x

• The formula used: Rate of the amount of heat flowing or heat current is given as:

$\frac {\Theta}{\Delta t} = K \times (\frac {A\Delta T}{x})$

Here, $\Delta \Theta$ is the amount of heat transferred, $\Delta T$ is the temperature difference, K is the thermal conductivity of the material, A is the area of cross-section of the material and x is the thickness or length of the material.

Now, for zero heat current in the rod, the temperature difference must be zero: $\Delta T = 0$

Since one end of the rod is maintained at 25°C, the other end must be maintained at 25°C. Hence heat current between A and C must be equal to the heat current between C and B

$(\frac {\Delta \theta}{\Delta t})_{AC} = (\frac {\Delta \theta}{\Delta t})_{CB}$

So, $K \times (\frac {A(\Delta T)_{AC}}{x}) = K \times (\frac {A(\Delta T)_{CB}}{1-x})$

Here $(\Delta T)_{AC}\ and\ (\Delta T)_{CB}$ is the temperature difference between AC and BC respectively.

So, $\frac {100 - 25}{x} = \frac {25 - 0}{1 - x}$

or $75(1-x) = 25x$

⇒75 - 75x = 25 x

⇒75 - 75x -25x = 0

$x = \frac {75}{100}$

or x = 0.75 m

Hence, in order to have zero heat current through the rod the other end of the rod must be placed at a distance of 0.75 m from the end at 100°C.