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 T1 and T2 be the thermometers to measure the temperature of the bar at a small distance x apart. Let thermometer T3 and T4 measure the temperature of outgoing and incoming water. To ensure good thermal contact, a small amount of mercury is laced into cavity.
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 T1 and T2 be the thermometers to measure the temperature of the bar at a small distance x apart. Let thermometer T3 and T4 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 θ1, θ2, θ3 and θ4 are the temperatures by T1, T2, T3, and T4, 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 (θ1 – θ2) t/ x ……… (i)
Where k is the thermal conductivity of metal bar and θ1-θ2 is the temperature difference between the cavities.
The temperature of water flowing through the copper tube rises from θ4 to θ3. So, the amount of heat absorbed by water in time t is
Q = m S (θ3 – θ4) ………. (ii)
From the principle of calorimetry,
Heat lost = heat gained
k A (θ1 – θ2) t/ x =m S (θ3 – θ4)
k = m S(θ3 – θ4)x / A(θ1 – θ2)t
which 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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