## Finding the Thermal Conductivity of a Good Conductor Using Searle's Bar

__ Apparatus __

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.

__ Method __

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 }.

__ Theory __

Assuming no loss of heat along the bar, it can be shown that:

where:

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 }).

__ Error Calculation __

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:.