**Experimental Determination of Thermal Conductivity of Solid Bar (Searle’s method)**

Let a metal bar XY whose conductivity is to be determined be enclosed with a steam chamber at one end and a copper tube around near the other end. Steam passes through the steam chamber and water passes through the copper tube at a constant rate. Let T

_{1}and T

_{2}be the thermometers to measure the temperature of the bar at a small distance x apart. Let thermometer T

_{3}and T

_{4}measure the temperature of outgoing and incoming water. To ensure good thermal contact, a small amount of mercury is laced into cavity.

As the end of the bar is heated by passing steam through steam chamber, so that heat is conducted from X to end Y and circulating water is warmed up. At steady state, the reading of all thermometers becomes constant. Heat lost from the surface of the bar is neglected because the bar is lagged by some non-conducting material.

Let θ

_{1}, θ_{2}, θ_{3}and θ_{4}are the temperatures by T_{1}, T_{2}, T_{3,}and T_{4}, respectively in steady-state.Area of cross section = A

Distance from cavities = x

Time for which the heat is considered = t

Mass of water that flows through metal bar in time t is,

Q = k A (θ

_{1}– θ_{2}) t/ x ……… (i)Where k is the thermal conductivity of metal bar and θ

_{1}-θ_{2}is the temperature difference between the cavities.The temperature of water flowing through the copper tube rises from θ

_{4}to θ_{3}. So, the amount of heat absorbed by water in time t isQ = m S (θ

_{3}– θ_{4}) ………. (ii)From the principle of calorimetry,

Heat lost = heat gained

k A (θ

_{1}– θ_{2}) t/ x =m S (θ_{3}– θ_{4}) k = m S(θ

_{3}– θ_{4})x / A(θ_{1}– θ_{2})twhich is required expression of thermal conductivity of a metal bar. As all the quantities in the above expression (right-hand side) are known, then k can be experimentally proved.

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