Finding the Thermal Conductivity of a Good Conductor Using Searle's Bar
Constant-head apparatus, measuring cylinder, stop watch, Searle's apparatus, steam generator, four thermometers T 1 , T 2 , T 3 , T 4 , Vernier callipers.
T 1 and T 2 measure the temperature at points on the bar, T 3 and T 4 measure the temperature of water entering and leaving the spiral C.
Adjust the constant-head device to give a steady flow of water through the coiled tube.
Pass steam from the steam generator through the steam chest. wait until the thermometers have reached a steady state (i.e. no significant increase or reduction of temperature for 10 minutes).
Measure T 1 , T 2 , T 3 and T 4 .
Measure the rate of water flow through the spiral by measuring the amount of water (m) collected in the measuring cylinder in a given time (t). Collect approximately 1 litre.
Using Vernier callipers, measure the diameter of the bar D and the distance d between the thermometers T 1 and T 2 .
Assuming no loss of heat along the bar, it can be shown that:
Q is the heat supplied to the bar in time t,
A is the cross-sectional area of the bar,
dT is the difference in temperature between two points in the bar dx apart,
k is the coefficient of thermal conductivity of the bar.
The heat Q warms up a mass m (in kilograms) of water from temperature T 4 to T 3 according to the formula:
where c is the specific heat capacity of water (c = 4190 J kg -1 K -1 ).
Using: ,(d in metres), and (A in metres squared) we obtain:
(in W m -1 K -1 ).
There is an error in assuming that no heat lost along the bar, but no correction has been made for this, although this will obviously affect the values of T 2 and T 1 .
The absolute error in each of the temperature differencesandis the sum of the absolute errors in reading the two thermometers.
Errors in m arise from errors in determining the mass of water collected.
Errors in the time t depend on the accuracy of the stop-watch.
Errors in measuring with the Vernier calliper are at least 0.05 mm, but may be bigger (estimate how precisely you can measure D and d).
The fractional error in k is given by:.