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# Thermal Conductivity of a Good Conductor by Searle’s Method

## Grade 11- physics -Transfer of Heat- Thermal conductivity if a Good conductor by Searle’s method

One of the best methods to determine the coefficient of thermal conductivity of a good conductor is Searle’s Method. The experimental arrangement is as shown in the figure.

It consists of a metal rod XY Whose coefficient of thermal conductivity is to be determined. The end X is enclosed in a steam chamber where steam is continuously passed to heat the rod. At the end Y, a copper tube is shouldered round the metal rod which absorbs the heat conducted through the rod. Water enters at the inlet I1 in the copper tube and leaves out the outlet I2, The temperature of water at the entrance is noted by thermometer T4 and at the exit by the thermometer T1 and T2. The rod is well covered with the non-conducting material like felt, cotton etc. To avoid conduction and convection of heat to the atmosphere.

As steam is passed into the steam chamber, the end X of the rod is heated and heat is conducted along the rod. The thermometers show the rise in temperature. IF it is heated continuously, a stage will come at which all thermometers will show constant temperature and steady-state flow of heat is reached. Let Θ1, Θ2, Θ3, Θ4 be the readings given by thermometers given by thermometers T1, T2, T3, T4 respectively in time t seconds. In steady state, the rate of heat flow through any section of the rod must be the same and so the amount of heat flowing per second through the rod C1 and C2 is equal to that absorbed by water flowing out through the copper tube at the same time. Then, the mass of water flowing out through the copper tube at the same time. Then, the mass of water flowing out per second through I2 is collected.

fig: Searle’s apparatus for the determination of thermal conductivity.

The amount of heat flowing through the metal rod from c1 and c2 in time t is given by

Q=KA(θ1θ2)tx(i)

$Q=\frac{KA\left({\theta }_{1}-{\theta }_{2}\right)t}{x}\dots \left(i\right)$

Amount of heat gained by water in time t is given by Q=MSw(θ4θ3)(ii)
where m is mass of water collected in time t and s is specific heat capacity of water
than from equation (i) and (ii)
KA(θ1θ2)tx=MSw(θ4θ3)

$\frac{KA\left({\theta }_{1}-{\theta }_{2}\right)t}{x}=M{S}_{w}\left({\theta }_{4}-{\theta }_{3}\right)$

K=MSw(θ4θ3)xA(θ1θ2)t
Hence the thermal conductivity k of the rod is determined.
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## Other equations and notes from the same chapter

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