Discuss Searle’s method to find the value of thermal conductivity.

Searle's method:
i) Searle's apparatus consists of a rod XY whose thermal conductivity is to be determined.
ii) One end X is enclosed in a steam chamber and steam is continuously passed through it. The second end Y is embedded in a cooling pipe C. A constant flow of water runs through pipe C.
iii) Two thermometers T₁ and T₂ are fitted in the holes drilled in the rod at P and Q separated by distance d.
iv) Two other thermometers T₃ and T₄ are used to measure the temperature of incoming and outgoing water through pipe C.
v) The rod is thoroughly insulated to stop any heat losses by radiation.
vi) Heat is conducted through the rod and when steady state is reached, the thermometers T₁ T₂, T₃ and T₄ record constant temperature.
vi) The mass of water flowing through a pipe C is collected in a given interval of time and weighed.
 

Now, it has been observed that at a steady state, the quantity of heat flowing through every section is same.
i.e., the rate of flow of heat at point P, Q and Y is same.

Quantity of heat that flows from section P to Q in one second is given by, 

           
where,
 θ₁ and θ₂ be the reading of thermometers T₁ and T₂ respectively.
Amount of heat gained by water in one second at end Y is,
              
where,
m is the mass of water collected in time t,
s be the specific heat and
₃ and θ₄ be the reading of thermometers T₃ and T_4. 
Now, equating (1) and (2), we get