Boyle-Mariotte Law - Revision history

Ist181114: /* Volume outside the seringe */

2017-08-15T18:40:23Z

Volume outside the seringe

Ist181114: /* Volume outside the seringe */

2017-08-15T18:31:16Z

Volume outside the seringe

Ist12916: /* Who likes this idea */

2014-02-25T09:14:01Z

Who likes this idea

Ist165721: /* Advanced Protocol */

2013-11-17T15:04:33Z

Advanced Protocol

Ist165721 at 12:49, 21 October 2013

2013-10-21T12:49:26Z

Ist165721 at 12:47, 21 October 2013

2013-10-21T12:47:55Z

Ist128595 at 22:11, 18 October 2013

2013-10-18T22:11:16Z

Ist128595 at 22:05, 18 October 2013

2013-10-18T22:05:15Z

Ist165721 at 23:11, 2 September 2013

2013-09-02T23:11:19Z

Ist165721 at 11:26, 21 April 2013

2013-04-21T11:26:13Z

@@ Line 61: / Line 61: @@
 We consider a volume \( V_0 \) added to the seringe volume and do the following procedure:
-# Run a few experiments (20, for example) with maximum diference between inicial and final volumes and maximum time between samples.
+# Run an experiments with a few samples (e.g. 20) with maximum diference between inicial and final volumes and maximum time between samples.
 # Fit the resulting data to a \( p = a/(V+ V_0) \) type function and determine both \( V_0 \) and \( a \) (which will be equal to \(nRT\) ).

@@ Line 61: / Line 61: @@
 We consider a volume \( V_0 \) added to the seringe volume and do the following procedure:
-# Run a few experiments (20, por example) with maximum diference between inicial and final volumes and maximum time between samples.
+# Run a few experiments (20, for example) with maximum diference between inicial and final volumes and maximum time between samples.
 # Fit the resulting data to a \( p = a/(V+ V_0) \) type function and determine both \( V_0 \) and \( a \) (which will be equal to \(nRT\) ).

@@ Line 20: / Line 20: @@
 =Who likes this idea=
-[[File:CienciaViva.gif|link=http://www.cienciaviva.pt/escolherciencia/|border|204px|border|204px]]
+[[File:EscolherCiencia.png|link=http://www.cienciaviva.pt/escolherciencia/|border|179px|border|179px]]
-[[File:ECB Logo.png|link=http://www.externatobenedita.net/|border|150px|border|150px]]
+[[File:ECB Logo.png|link=http://www.externatobenedita.net/|border|179px|border|179px]]
 [[File:Logo_alberto_cores.jpg|link=http://www.es-al-berto.com/|border|120px|border|120px]]
 [[File:LogoAEA_800x132.jpg|link=http://aealvalade.edu.pt/|border|280px|border|280px]]
@@ Line 29: / Line 29: @@
 The first school involved in this experiment were Escola Secundária Padre António Vieira, Alvalade/Lisboa and Externato Cooperativo da Benedita, Leiria. Escola Secundária Poeta Al Berto in Sines also colaborated.
 =Experimental Apparatus=

@@ Line 54: / Line 54: @@
 =Advanced Protocol=
-With a high enough time between samples, it is also possible to determine the Ideal Gas Constant, if we consider room temperature to be 22ºC.
+With a high enough time between samples we can consider the transformation to be isothermal (i.e. the temperature inside the seringe doesn't change).
 Procedure:
@@ Line 62: / Line 74: @@
 # Compare the R value that was found through this method with the one found through the average product of \( pV \) (using a math software, determine the product between p and V for each line and then find the average).
 # Find one last estimate for R setting the exponent at -1 (i.e., fitting the data to a \( a x ^{-1} \) function).
 =Links=
 *[[Lei de Boyle-Mariotte | Portuguese version (Versão em Português)]]

← Older revision		Revision as of 12:49, 21 October 2013
Line 19:		Line 19:


		+	=Who likes this idea=
		+	[[File:CienciaViva.gif\|link=http://www.cienciaviva.pt/escolherciencia/\|border\|204px\|border\|204px]]
		+	[[File:ECB Logo.png\|link=http://www.externatobenedita.net/\|border\|150px\|border\|150px]]
		+	[[File:Logo_alberto_cores.jpg\|link=http://www.es-al-berto.com/\|border\|120px\|border\|120px]]
		+	[[File:LogoAEA_800x132.jpg\|link=http://aealvalade.edu.pt/\|border\|280px\|border\|280px]]
		+
		+
		+	This idea is the result of the PEC26 contract with Ciência Viva - The portuguese Agency for Cientific and technological Culture and its objectives are (i) sharing (through the internet) existing experimental setups that some high-schools have but are not in use and (ii) promote teaching cience through the use of experimental activities. The automation of the experiment was made by IST students as part of the e-lab project.

−	~~=Who likes~~ this ~~idea=~~	+	The first school involved in this experiment were Escola Secundária Padre António Vieira, Alvalade/Lisboa and Externato Cooperativo da Benedita, Leiria. Escola Secundária Poeta Al Berto in Sines also colaborated.
−	~~[[File:CienciaViva~~.~~gif\|border\|204px\|border\|204px]]~~

@@ Line 20: / Line 20: @@
 =Experimental Apparatus=
-The apparatus is composed by a cylinder (5 ml syringe) filled with air whose plunger is displaced by a servo motor.
+The apparatus is composed by a cylinder (5 ml syringe) filled with air, whose plunger is displaced by a servo motor.
 [[File:Boyle-mariotte-montagem.jpg|thumb|alt=Experimental setup|Setup]]
-It's possible to choose the compression/expansion limits  of the chamber and measure the air pressure and volume inside it during the plunger's motion. The speed at which the transformation occurs can also be specified by choosing the time between samples.
+It is possible to choose the compression/expansion limits  of the chamber and measure the air pressure and volume inside it during the plunger's motion. The speed at which the transformation occurs can also be specified by choosing the time between samples.
@@ Line 36: / Line 36: @@
 [[File:Boyle-mariotte-graf1.png|thumb|Graphical fit with experimental results with 1 sec. between samples.]]
-If the time between samples is decreased (i.e. the process is faster), the transformation is no longer isothermal and becomes slightly adiabatic, because there is not enough time for the heat exchange between the inside of the cylinder and the environment. This way, the compression no longer follows the Boyle-Mariotte, a fact that is clearly demonstrated by the deviation from the power function, which would be \( ^3/_5 \) in the ideal case (\( \gamma ^{-1} = \frac{c_v}{c_p} \)).
+If the time between samples is decreased (i.e. the process is faster), the transformation is no longer isothermal and becomes slightly adiabatic, because there is not enough time for the heat exchange between the inside of the cylinder and the environment. This way, the compression no longer follows the Boyle-Mariotte Law, a fact that is clearly demonstrated by the deviation from the power function, which would be \( ^3/_5 \) in the ideal case (\( \gamma ^{-1} = \frac{c_v}{c_p} \)).
 It is difficult to obtain a fast enough compression to achieve this value, since thermalization occurs quickly (in the order of the sound speed). However this can be used to study how the transformation speed influences the deviation between the experimental data and the Boyle-Mariotte Law.
@@ Line 48: / Line 48: @@
 # Fit the experimental data to a \( a x ^b \) type function and find the proportion constant (which will equal \( nRT \)).
 # Assume the room temperature to be 22ºC. Determine the amount of substance (in mole) present at the inicial stage of the experiment ( \( 5 ml \) of air at NTP conditions). Find R.
-# Compare the value for R that was found through this method with the one found through the average product of \( pV \) (using a math software, determine the product between p and V for each line and then find the average).
+# Compare the R value that was found through this method with the one found through the average product of \( pV \) (using a math software, determine the product between p and V for each line and then find the average).
 # Find one last estimate for R setting the exponent at -1 (i.e., fitting the data to a \( a x ^{-1} \) function).

@@ Line 24: / Line 24: @@
 [[File:Boyle-mariotte-montagem.jpg|thumb|alt=Experimental setup|Setup]]
-It's possible to choose the limits for the compression/expansion of the chamber and measure the air pressure and volume inside it during the plunger's motion. The speed at which the transformation occurs can also be specified by choosing the time between samples.
+It's possible to choose the compression/expansion limits  of the chamber and measure the air pressure and volume inside it during the plunger's motion. The speed at which the transformation occurs can also be specified by choosing the time between samples.
@@ Line 30: / Line 30: @@
 The user must specify the initial and final volume, the number of samples and time interval between them. This last option indirectly defines the speed at which the transformation occurs.
-If the experiment is executed with a long time interval between samples the transformation is close to isothermal. That means the air temperature inside the syringe doesn't change and Boyle-Mariotte Law is applicable.
+If the experiment is executed with a long time interval between samples, the transformation is close to isothermal. That means the air temperature inside the syringe doesn't change and the Boyle-Mariotte Law is applicable.
-The example bellow is such a case where we can verify that the product \( pV \) is, in average, \( 49,3 \pm 0,3 l.kPa \), close to the theoretical value of \( nRT \) (where \( n = 2 \times 10 ^{-4} mol\), equivalent to the full syringe volume at rest \( 5 ml \), PTN).
+The example bellow is one such case where we can verify that the product \( pV \) is, in average, \( 49,3 \pm 0,3 l.kPa \), close to the theoretical value of \( nRT \) (where \( n = 2 \times 10 ^{-4} mol\), equivalent to the full syringe volume at rest \( 5 ml \), PTN).
 [[File:Boyle-mariotte-graf1.png|thumb|Graphical fit with experimental results with 1 sec. between samples.]]
-If the time between samples is decreased (i.e. the process is faster), the transformation is no longer isothermal and becomes slight adiabatic, because there is not enough time for heat exchange between the inside of the cylinder and the environment. In this way, the compression no longer follows the Boyle-Mariotte, a fact that is clearly demonstrated by the deviation from the power function, which would be \( ^3/_5 \) in the ideal case (\( \gamma ^{-1} = \frac{c_v}{c_p} \)).
+If the time between samples is decreased (i.e. the process is faster), the transformation is no longer isothermal and becomes slightly adiabatic, because there is not enough time for the heat exchange between the inside of the cylinder and the environment. This way, the compression no longer follows the Boyle-Mariotte, a fact that is clearly demonstrated by the deviation from the power function, which would be \( ^3/_5 \) in the ideal case (\( \gamma ^{-1} = \frac{c_v}{c_p} \)).
-It is difficult to obtain a fast enough compression to achieve this value, since thermalization occurs quickly (in the order of the speed of sound). However this can be used to study how the transformation speed influences the deviation between the experimental data and Boyle-Mariotte Law.
+It is difficult to obtain a fast enough compression to achieve this value, since thermalization occurs quickly (in the order of the sound speed). However this can be used to study how the transformation speed influences the deviation between the experimental data and the Boyle-Mariotte Law.
@@ Line 49: / Line 49: @@
 # Assume the room temperature to be 22ºC. Determine the amount of substance (in mole) present at the inicial stage of the experiment ( \( 5 ml \) of air at NTP conditions). Find R.
 # Compare the value for R that was found through this method with the one found through the average product of \( pV \) (using a math software, determine the product between p and V for each line and then find the average).
-# Find one last estimate for R find setting the exponent at -1 (i.e., fitting the data to a \( a x ^{-1} \) function).
+# Find one last estimate for R setting the exponent at -1 (i.e., fitting the data to a \( a x ^{-1} \) function).

@@ Line 3: / Line 3: @@
-<div class="toccolours mw-collapsible mw-collapsed" style="width:320px">
+<div class="toccolours mw-collapsible mw-collapsed" style="width:420px">
 '''Links'''
 <div class="mw-collapsible-content">