KeterehskyLab: Experiment 5 Heat Transfer

Experiment 5 Heat Transfer

Topic: Heat Transfer

Title: Thermal conductivity

Objective: To determine the thermal conductivity of glass

Theory:

The rate of heat flow through a conductor is expressed as

$<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>d</mi><mi>Q</mi></mrow><mrow><mi>d</mi><mi>t</mi></mrow></mfrac><mo>=</mo><mo>-</mo><mi>k</mi><mi>A</mi><mfrac><mrow><mi>d</mi><mi>θ</mi></mrow><mrow><mi>d</mi><mi>t</mi></mrow></mfrac></math>$ (1)

Where k is the thermal conductivity, A cross-sectional area of the conductor and $<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>d</mi><mi>θ</mi></mrow><mrow><mi>d</mi><mi>t</mi></mrow></mfrac></math>$ the temperature gradient.

Rate of heat flow from the warm water with temperature 0 in the boiling tube to the surrounding is given by

........ (2)

wherem is the mass of water, c the specific heat capacity of water anddθdtthe rate of cooling.

Equating (1) and (2)

mc dθdt= -kAdθdx ........ (3)

From equation (3), if the surrounding temperature is 0 °C the relationship between temperature θ and time t is given by

= -ktBrx+ 0 ,

wheret is in second, 0 the initial temperature, B is 2.1 X 106 J m-3K-1, r the average radius of the boiling tube, and x the thickness of the wall of the boiling tube.

Apparatus:

i. A boiling tube

ii. A thermometer (-10 °C - 110 °C)

iii. A 1000 cm3 beaker

iv. Two stirrers

v. A cork stopper

vi. A stopwatch

vii. A pair of vernier calipers

viii. A retort stand and clamp

ix. Ice cubes 

x. Warm water 

Procedure:

(a) Measure and record the internal and external diameters of a boiling tube and hence calculate the average radius r and the thickness x of the wall of the boiling tube.

(b) Fill up a beaker with water and ice. Clamp the boiling tube on to a retort stand and lower the boiling tube into the beaker until the whole of the boiling tube almost submerge in ice and water mixture as shown in the Figure 5.

Figure 5

(c) Pour warm water into the boiling tube until the water level inside the tube reaches about 1 cm below the ice-water level in the beaker. The temperature of the ice and water mixture inside the beaker should be 0 °C before the warm water is poured into the boiling tube.

(d) Insert the stirrer and thermometer through the cork stopper as shown in Figure 5.

(e) Record time t and the corresponding temperature θ starting at temperature around θ = 30 °C. Record time t and temperature until the temperature in the boiling tube reaches about 5 °C. The ice-water mixture in the beaker and warm water in the boiling tube should be constantly stirred throughout the experiment.

(f} Plot a graph of In θ against t.

(g) Determine the thermal conductivity of the glass. or alternative