Thermal Conductivity of Metals - Revision history

Ist165721: Text replacement - "\]" to ""

2015-05-24T19:50:57Z

Text replacement - "\]" to "</math>"

Ist165721: Text replacement - "\[" to " $"$

2015-05-24T18:45:37Z

Text replacement - "\[" to "<math>"

Ist12916: /* Experimental Apparatus */

2013-11-28T10:01:48Z

Experimental Apparatus

Ist12916: /* Experimental Apparatus */

2013-11-27T16:25:29Z

Experimental Apparatus

Ist12916: /* Advanced Protocol */

2013-11-27T10:15:18Z

Advanced Protocol

Ist128595 at 16:27, 19 October 2013

2013-10-19T16:27:10Z

Ist128595 at 16:14, 19 October 2013

2013-10-19T16:14:31Z

Ist165721 at 16:03, 12 March 2013

2013-03-12T16:03:17Z

Ist167944: /* Advanced Protocol */

2012-11-12T13:53:01Z

Advanced Protocol

Ist167944: /* Advanced Protocol */

2012-11-12T12:32:56Z

Advanced Protocol

@@ Line 61: / Line 61: @@
 <math>
 k = \frac{C_p \rho n \omega (x_1 - x_2)^2}{2 (\phi_1 - \phi_2) ln(A_1/A_2)}
-\]
+</math>
 where \( C_p \) is the metal's heat capacity, \( \rho \) the density, \( \omega \) the angular frequency, \( (x_2 - x_1) \) the distance between thermometers, \( (\phi_1 - \phi_2) \) phase between signals (measured in radians) and \( A_1/A_2 \) the ratio between amplitudes.

@@ Line 59: / Line 59: @@
 The thermal conductivity of each metal can be determined from the experimental data by using:
-\[
+<math>
 k = \frac{C_p \rho n \omega (x_1 - x_2)^2}{2 (\phi_1 - \phi_2) ln(A_1/A_2)}
 \]

@@ Line 29: / Line 29: @@
 [[File:Conducao-montagem.jpg|thumb|Montagem: Mineral wool sandwich covering the metal cylinders.]]
-The first 7mm of each bar are wrapped in a heating resistor. 10mm away from the heat sink is the first batch of thermometers, the second being at 250mm and the third at 300mm. The heat sink keeps one of the ends at room temperature and is the position axis reference point. The bars are mounted in the middle of two 50mm thick layers of thermal insulation material (mineral wool) that prevent heat convection and minimize thermal losses.
+The first 70mm of each bar are wrapped with an heating resistor which occupies 2,5mm on it's center. In the opposite side is placed a refrigerated heat sink to keep this end at room temperature and is the position axis reference point. 10mm away from the heat sink is the first batch of thermometers, the second being at 160mm and the third at 210mm.  The bars are mounted in the middle of two 50mm thick layers of thermal insulation material (mineral wool) that prevent heat convection and minimize thermal losses.
 In a pulsed or periodic regime, an electric current is applied to the heating resistor that heats that end through Joule's effect. The heat generated will run through the bar and will be dissipated at the opposite end in the sink.

@@ Line 29: / Line 29: @@
 [[File:Conducao-montagem.jpg|thumb|Montagem: Mineral wool sandwich covering the metal cylinders.]]
-The first 70mm of each bar are wrapped in a heating resistor. 10mm away from the heat sink is the first batch of thermometers, the second being at 250mm and the third at 300mm. The heat sink keeps one of the ends at room temperature and is the position axis reference point. The bars are mounted in the middle of two 50mm thick layers of thermal insulation material (mineral wool) that prevent heat convection and minimize thermal losses.
+The first 7mm of each bar are wrapped in a heating resistor. 10mm away from the heat sink is the first batch of thermometers, the second being at 250mm and the third at 300mm. The heat sink keeps one of the ends at room temperature and is the position axis reference point. The bars are mounted in the middle of two 50mm thick layers of thermal insulation material (mineral wool) that prevent heat convection and minimize thermal losses.
 In a pulsed or periodic regime, an electric current is applied to the heating resistor that heats that end through Joule's effect. The heat generated will run through the bar and will be dissipated at the opposite end in the sink.
 By choosing the pulse width (it should be around one minute), heat propagation can be observed by measuring the three points described above.
 =Protocol=

@@ Line 64: / Line 64: @@
 \]
-where \( C_p \) is the metal's heat capacity, \( \rho \) the density, \( \omega \) the angular frequency, \( (x_2 - x_1) \) the distance between thermometers, \( (f_1 - f_2) \) phase between signals (measured in radians) and \( A_1/A_2 \) the ratio between amplitudes.
+where \( C_p \) is the metal's heat capacity, \( \rho \) the density, \( \omega \) the angular frequency, \( (x_2 - x_1) \) the distance between thermometers, \( (\phi_1 - \phi_2) \) phase between signals (measured in radians) and \( A_1/A_2 \) the ratio between amplitudes.
 We can also calculate the ''k'' experimental uncertainty by using propagation formulas.
@@ Line 96: / Line 96: @@
 |81
 |}
 =Links=
 *[[Determinação da Condutividade Térmica em Metais | Portuguese Version (Versão em português)]]

@@ Line 25: / Line 25: @@
 # Comparison of the output of each bar's first sensor.
-Each bar has  a 5mm diameter and is 370mm long and each one is made of a different metal: iron, copper and brass.
+Each bar is 370mm long and has a 5mm diameter and each one is made of a different metal: iron, copper and brass.
 [[File:Conducao-montagem.jpg|thumb|Montagem: Mineral wool sandwich covering the metal cylinders.]]
-The first 70mm of each bar are wrapped in a heating resistor. 10mm away from the heat sink is the first batch of thermometers, the second being at 250mm and the third at 300mm. The heat sink keeps one of the ends at room temperature and is the reference point for the position axis. The bars are mounted in the middle of two 50mm thick layers of thermal insulation material (mineral wool) that prevent heat convection and minimize thermal losses.
+The first 70mm of each bar are wrapped in a heating resistor. 10mm away from the heat sink is the first batch of thermometers, the second being at 250mm and the third at 300mm. The heat sink keeps one of the ends at room temperature and is the position axis reference point. The bars are mounted in the middle of two 50mm thick layers of thermal insulation material (mineral wool) that prevent heat convection and minimize thermal losses.
-In a pulsed or periodic regime, an electric current is applied to the heating resistor that heats that end through Joule's effect. The heat generated will run through the bar and be dissipated at the opposite end in sink.
+In a pulsed or periodic regime, an electric current is applied to the heating resistor that heats that end through Joule's effect. The heat generated will run through the bar and will be dissipated at the opposite end in the sink.
-By choosing the pulse width (it should be around one minute), heat propagation can be observed by measuring the three points described earlier.
+By choosing the pulse width (it should be around one minute), heat propagation can be observed by measuring the three points described above.
@@ Line 39: / Line 39: @@
 Run the experiment in pulse mode and observe how the pulse travels along the bars.
-'''Note:''' The heat sink keeps the ends of the bars at room temperature, which means that the readings of one of the thermometers will not vary, having been chosen as the reference point for distance.
+'''Note:''' The heat sink keeps the ends of the bars at room temperature, which means that the readings of one of the thermometers will not vary, having been chosen as the distance reference point.
@@ Line 52: / Line 52: @@
 For best results, please follow the procedure:
-# Execute two experiments in periodic mode, selecting a time interval of a few seconds between samples and a heating time of the order of one minute. For the first run, choose the maximum acquisition time possible, and for the second choose a reasonable value based on the data from the first.
+# Execute two experiments in periodic mode, selecting a time interval of a few seconds between samples and a heating time of approximately one minute. For the first run, choose the maximum acquisition time possible, and for the second choose a reasonable value based on the data from the first one.
 # Copy the data to a spreadsheet or preferably to a science application, like Matlab or Origin;
 # Fit a math function to the thermal behavior of the bar;
@@ Line 66: / Line 66: @@
 where \( C_p \) is the metal's heat capacity, \( \rho \) the density, \( \omega \) the angular frequency, \( (x_2 - x_1) \) the distance between thermometers, \( (f_1 - f_2) \) phase between signals (measured in radians) and \( A_1/A_2 \) the ratio between amplitudes.
-We can also calculate the experimental uncertainty that ''k'' has, by using propagation formulas.
+We can also calculate the ''k'' experimental uncertainty by using propagation formulas.
 Note: the diameter of the bars was measured up to a ''0.01 mm'' and the sensor position up to ''0.5 mm''.

@@ Line 1: / Line 1: @@
 =Description of the Experiment=
 This experiment revolves around the conduction of heat. The user can study and compare how fast heat propagates through three bars of different materials.
 <swf height="200" width="500">http://www.elab.tecnico.ulisboa.pt/anexos/descricoes-flash/ConducaoCalorFinal.swf</swf>
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 By choosing the pulse width (it should be around one minute), heat propagation can be observed by measuring the three points described earlier.
 =Protocol=
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 |81
 |}

@@ Line 56: / Line 56: @@
 Afterwards, compare it to the textbook value.
-There is a simple analysis that can be made to check the experimental data, assuming the initial stimulus is sinusoidal. This way we can take ''n=1'' and the phase shift is determined by the distance between the extrema of the experimental data.
+A simple analysis can be done to check the experimental data, assuming the initial stimulus is sinusoidal. This way we can take ''n=1'' and the phase shift is determined by the distance between the maximum of the two experimental curves.
 {| border="1" style="text-align: center;"

@@ Line 37: / Line 37: @@
 For best results, please follow the procedure:
-# Execute two experiments in pulsed mode, selecting an interval of a few seconds between samples and a heating about a minute. In the first run, choose the maximum possible recording time and, after looking at these, do the second with a recording time depending on the results of the first;
+# Execute two experiments in periodic mode, selecting a time interval of a few seconds between samples and a heating time of the order of one minute. For the first run, choose the maximum acquisition time possible, and for the second choose a reasonable value based on the data from the first.
-# Copy to the data to a spreadsheet or a science application, like Matlab or Origin;
+# Copy the data to a spreadsheet or preferably to a science application, like Matlab or Origin;
 # Fit a math function to the thermal behavior of the bar;
 # Determine the period of oscillation for each experiment conducted and the phase shift between two consecutive thermometers, for each metal available;
 # Numerically adjust the function to the experimental data to get the highest precision possible.
-The value for the thermal conductivity of each metal can be determined from the experimental data by using:
+The thermal conductivity of each metal can be determined from the experimental data by using:
 \[

Thermal Conductivity of Metals - Revision history

Ist165721: Text replacement - "\]" to ""

Ist165721: Text replacement - "\[" to ""

Ist12916: /* Experimental Apparatus */

Ist12916: /* Experimental Apparatus */

Ist12916: /* Advanced Protocol */

Ist128595 at 16:27, 19 October 2013

Ist128595 at 16:14, 19 October 2013

Ist165721 at 16:03, 12 March 2013

Ist167944: /* Advanced Protocol */

Ist167944: /* Advanced Protocol */

Ist165721: Text replacement - "\[" to " $"$