Home Page Image

Name:

Michael Lee

Occupation:

Student of University of Calgary studying in the electrical and biomedical engineering department

 

 

My partner Links:

gmecha.com

realestate43.com

ngemu.com
 
biomedical career engineering in technology, career in biomedical engineering 20, career information in biomedical engineering, mechanical engineering degree online, online degree engineering, online engineering bachelor degree, biomedical career engineering in technology, career in biomedical engineering 20, career information in biomedical engineering, mechanical engineering degree online, online degree engineering, online engineering bachelor degree, biomedical career engineering in technology, career in biomedical engineering 20, career information in biomedical engineering, mechanical engineering degree online, online degree engineering, online engineering bachelor degree, biomedical career engineering in technology, career in biomedical engineering 20, career information in biomedical engineering, mechanical engineering degree online, online degree engineering, online engineering bachelor degree, biomedical career engineering in technology, career in biomedical engineering 20, career information in biomedical engineering, mechanical engineering degree online, online degree engineering, online engineering bachelor degree, biomedical career engineering in technology, career in biomedical engineering 20, career information in biomedical engineering, mechanical engineering degree online, online degree engineering, online engineering bachelor degree, biomedical career engineering in technology, career in biomedical engineering 20, career information in biomedical engineering, mechanical engineering degree online, online degree engineering, online engineering bachelor degree, biomedical career engineering in technology, career in biomedical engineering 20, career information in biomedical engineering, mechanical engineering degree online, online degree engineering, online engineering bachelor degree, biomedical career engineering in technology, career in biomedical engineering 20, career information in biomedical engineering, mechanical engineering degree online, online degree engineering, online engineering bachelor degree, biomedical career engineering in technology, career in biomedical engineering 20, career information in biomedical engineering, mechanical engineering degree online, online degree engineering, online engineering bachelor degree, biomedical career engineering in technology, career in biomedical engineering 20, career information in biomedical engineering, mechanical engineering degree online, online degree engineering, online engineering bachelor degree, biomedical career engineering in technology, career in biomedical engineering 20, career information in biomedical engineering, mechanical engineering degree online, online degree engineering, online engineering bachelor degree, biomedical career engineering in technology, career in biomedical engineering 20, career information in biomedical engineering, mechanical engineering degree online, online degree engineering, online engineering bachelor degree, biomedical career engineering in technology, career in biomedical engineering 20, career information in biomedical engineering, mechanical engineering degree online, online degree engineering, online engineering bachelor degree, biomedical career engineering in technology, career in biomedical engineering 20, career information in biomedical engineering, mechanical engineering degree online, online degree engineering, online engineering bachelor degree, biomedical career engineering in technology, career in biomedical engineering 20, career information in biomedical engineering, mechanical engineering degree online, online degree engineering, online engineering bachelor degree, biomedical career engineering in technology, career in biomedical engineering 20, career information in biomedical engineering, mechanical engineering degree online, online degree engineering, online engineering bachelor degree, biomedical career engineering in technology, career in biomedical engineering 20, career information in biomedical engineering, mechanical engineering degree online, online degree engineering, online engineering bachelor degree, biomedical career engineering in technology, career in biomedical engineering 20, career information in biomedical engineering, mechanical engineering degree online, online degree engineering, online engineering bachelor degree, biomedical career engineering in technology, career in biomedical engineering 20, career information in biomedical engineering, mechanical engineering degree online, online degree engineering, online engineering bachelor degree, biomedical career engineering in technology, career in biomedical engineering 20, career information in biomedical engineering, mechanical engineering degree online, online degree engineering, online engineering bachelor degree, biomedical career engineering in technology, career in biomedical engineering 20, career information in biomedical engineering, mechanical engineering degree online, online degree engineering, online engineering bachelor degree, biomedical career engineering in technology, career in biomedical engineering 20, career information in biomedical engineering, mechanical engineering degree online, online degree engineering, online engineering bachelor degree, biomedical career engineering in technology, career in biomedical engineering 20, career information in biomedical engineering, mechanical engineering degree online, online degree engineering, online engineering bachelor degree, biomedical career engineering in technology, career in biomedical engineering 20, career information in biomedical engineering, mechanical engineering degree online, online degree engineering, online engineering bachelor degree, biomedical career engineering in technology, career in biomedical engineering 20, career information in biomedical engineering, mechanical engineering degree online, online degree engineering, online engineering bachelor degree, biomedical career engineering in technology, career in biomedical engineering 20, career information in biomedical engineering, mechanical engineering degree online, online degree engineering, online engineering bachelor degree, biomedical career engineering in technology, career in biomedical engineering 20, career information in biomedical engineering, mechanical engineering degree online, online degree engineering, online engineering bachelor degree, biomedical career engineering in technology, career in biomedical engineering 20, career information in biomedical engineering, mechanical engineering degree online, online degree engineering, online engineering bachelor degree, biomedical career engineering in technology, career in biomedical engineering 20, career information in biomedical engineering, mechanical engineering degree online, online degree engineering, online engineering bachelor degree, biomedical career engineering in technology, career in biomedical engineering 20, career information in biomedical engineering, mechanical engineering degree online, online degree engineering, online engineering bachelor degree, biomedical career engineering in technology, career in biomedical engineering 20, career information in biomedical engineering, mechanical engineering degree online, online degree engineering, online engineering bachelor degree, biomedical career engineering in technology, career in biomedical engineering 20, career information in biomedical engineering, mechanical engineering degree online, online degree engineering, online engineering bachelor degree, biomedical career engineering in technology, career in biomedical engineering 20, career information in biomedical engineering, mechanical engineering degree online, online degree engineering, online engineering bachelor degree,



Treatment of Data

Table 4: Pv of the pure substances


Temperature (°C)

Ethanol Pv (mmHg)

Ethanol Pv
(kPa)

n-Propanol Pv (mmHg)

n-Propanol Pv
(kPa)

56

286

38.1238

 

 

58

314

41.8562

 

 

60

344

45.8552

 

 

62

377

50.2541

 

 

64

412

54.9196

 

 

66

450

59.985

 

 

68

490

65.317

 

 

70

534

71.1822

 

 

72

581

77.4473

 

 

74

631

84.1123

286

38.1238

76

658

87.7114

300

39.99

78

 

 

343

45.7219

80

 

 

374

49.8542

82

 

 

408

54.3864

84

 

 

444

59.1852

86

 

 

483

64.3839

88

 

 

525

69.9825

90

 

 

570

75.981

Table 5:Logarithm of Vapor Pressure at different temperatures


1/T
(Kelvins)-1

Logarithm of vapour pressure of Ethanol
ln(Pv)

Logarithm of vapour pressure of n-Propanol
ln(Pv)

0.003038

3.640839

 

0.00302

3.73424

 

0.003002

3.825489

 

0.002984

3.917092

 

0.002966

4.00587

 

0.002949

4.094095

 

0.002931

4.179252

 

0.002914

4.265243

 

0.002897

4.349598

 

0.002881

4.432153

3.640839

0.002864

4.474052

3.688629

0.002848

 

3.822577

0.002832

 

3.909103

0.002816

 

3.996114

0.0028

 

4.080672

0.002784

 

4.164864

0.002769

 

4.248245

0.002754

 

4.330483

Treatment of Data

1.1 To find the vapour pressure

Formula: a
Symbol:
Pv   = vapor pressure (kPa)
Pb   = corrected barometric pressure (kPa)
DP = The pressure difference between the two legs of the manometers (kPa)

Sample calculation for pure ethanol at 56°C
                                                                                                                 DP=379mmHg
Pb =665.0mmHg

a
a
a

Note: This answer has to be converted into kPa, to convert the values, one must multiply the answer with the conversion factor of 0.1333.
Converting it into kPa
Pv(kPa) = Pv(mmHg) x 0.1333
Pv(kPa) = 286.0mmHg x 0.1333
Pv(kPa) = 38.12kPa

Sample calculation for pure n-propanol at 74°C
                                                                                                                 DP=379mmHg
Pb =665.0mmHg

a
a
a

Note: This answer has to be converted into kPa, to convert the values, one must multiply the answer with the conversion factor of 0.1333.
Converting it into kPa
Pv(kPa) = Pv(mmHg) x 0.1333
Pv(kPa) = 286.0mmHg x 0.1333
Pv(kPa) = 38.12kPa

 

 

1.2 To find the natural log of the vapor pressure in kPa
Formula: ln(Pv)
Symbol:
ln(): Natural log function
Pv: Vapor pressure (kPa)
This formula is for taking the natural log of the vapor pressure.

Sample calculation for Ethanol at 56°C
Pv= 38.12kPa
ln(Pv)
ln(38.12kPa)=3.64

Sample calculation for n-Propanol at 74°C
Pv= 38.12kPa
ln(Pv)
ln(38.12kPa)=3.64

 

1.3 To find the inverse of temperature
Formula: T-1=1/T
Symbols:
T-1= inverse of temperature (K-1)
T  = Temperature (K)

Note: Temperature in Table 1 is in degrees Celsius. To convert degrees Celsius into Kelvins, one must add the temperature in Celsius by 273.15K to obtain the temperature in Kelvins.

 

Sample calculations for 56°C
T-1=1/T
T-1= 1/(56+273.15K)
T-1= 0.003038K-1

 

 

 

1.4 To find coeffiecient A
Formula: a
Symbol:
A   = Constant (K)
Dy = Change of y coordinate ln(Pv)
Dx = Change of x coordinate (K-1)

This formula is derived from the original slope formula:
a. Using the line of best fit, one can find an approximation value for coefficient A.

Sample calculation for ethanol
Two points from line of best fit (0.00286, 4.476) and (0.0030, 3.83)
a
                   or
-A=   linear regression by input the x (Inverse temperature) and y (ln(Pv) values on Table 4 in calculator and use the function LinReg(Ax+B)

A= 4907.94K

Sample calculation for n-propanol
Two points from line of best fit (0.00285, 3.82) and (0.00277, 4.25)
a
                   or
-A=   linear regression by input the x (Inverse temperature) and y (ln(Pv) values on Table 4 in calculator and use the function LinReg(Ax+B)

A= 5554.37K

 

 

 

 

 

 

1.5 To find coefficient C
Formula: a
Symbol:
ln(Pv): The natural log of pressure
       T: The temperature at certain pressure (K)
       A: Coefficient (K)
       C: Coefficient
This equation is from the relationship between vapor pressure and temperature.

Sample Calculation for ethanol at 56°C
                                                                    ln(Pv)=3.64                            
                                                                                  A=4907.94K
T=56°C+273.15K=329.15K

a
a
a

Sample Calculation for n-propanol at 74°C
                                                                    ln(Pv)=3.64                            
                                                                                  A=5554.37K
T=74°C+273.15K=347.15K

a
a
a

 

 

 

 

 

 

1.6 To find the latent heat vaporization
Formula: a
Symbol:
    A= Constant (K)
DHv= Latent heat of vaporization (kJ/kg)
    R= Universal gas constant (8.314kJ/molK)

This formula is derived from the relationship between the parameter A, the gas constant, and DHv. If parameter A is known, one can find the latent heat of vaporization using the above formula.

Sample Calculation for ethanol
                                                                                                              A= 4907.94K
R=8.314kJ/molK
a
a
a

Sample Calculation for n-propanol
                                                                                                              A= 5554.37K
R=8.314kJ/molK
a
a
a

 

Note: The latent heat should be in kJ/kg. To convert the units into kJ/kg, one must divide the above value by the molar mass.

Ethanol:
a

n-Propanol:
a

 

 

1.7 To find the normal boiling point
Formula: a
Symbol:
ln(Pv)= the natural log of pressure
Tb=Normal boiling point (K)
A =Coefficient (K)
C =Coefficient

This equation is from the relationship between vapor pressure and temperature. By knowing the values of A, C and the vapor pressure at normal boiling point (101.325kPa), one can find the value for the normal point using the equation above.

Sample Calculation for ethanol
Pv=101.325kPa
                                                                                                                       A= 4907.94K
                                                                                                                a
a
 a
a

Sample Calculation for n-propanol
Pv=101.325kPa
                                                                                                                       A= 5554.37K
                                                                                                                a
a
 a
a

 

 

 

 

 

1.8 To find Percentage of Error
Formula: a
This formula is to calculate the percentage of error by finding the difference between theoretical and experimental value, and then divide by the theoretical value multiply by 100% to obtain the percentage.

Sample calculation for DHv of Ethanol
Acquired Value: 885.71kJ/kg
Accepted Value: 838.00kJ/kg
a

 

a

a

 

Table 6: Percentage of Error

 

%Error (%)

DHv of Ethanol

5.69

DHv of n-Propanol

 

Tb of Ethanol

1.06

Tb of n-Propanol

0.05

 

      Table 7: Vapour pressure of different mixtures in different temperature

 

Liquid Mixture Composition (Volumes of Ethanol: Volumes of n-Propanol)

Temperature (°C)

1:0 (kPa)

8:1 (kPa)

4:1 (kPa)

1:1 (kPa)

1:4 (kPa)

1:8 (kPa)

0:1 (kPa)

56

38.1238

 

 

 

 

 

 

58

41.8562

40.2566

38.9236

 

 

 

 

60

45.8552

44.1223

42.656

 

 

 

 

62

50.2541

48.3879

46.7883

39.8567

 

 

 

64

54.9196

52.9201

51.1872

43.7224

 

 

 

66

59.985

57.8522

55.986

47.8547

 

 

 

68

65.317

63.0509

61.0514

52.2536

39.5901

 

 

70

71.1822

68.7828

66.5167

57.0524

43.4558

38.5237

 

72

77.4473

74.9146

72.5152

62.2511

47.4548

42.1228

 

74

84.1123

81.313

78.7803

67.7164

51.8537

46.1218

38.1238

76

87.7114

84.7788

82.2461

70.649

54.2531

48.2546

39.99

78

 

 

 

80.1133

61.7179

54.9196

45.7219

80

 

 

 

86.7783

67.0499

59.8517

49.8542

82

 

 

 

 

72.9151

65.0504

54.3864

84

 

 

 

 

79.0469

70.649

59.1852

86

 

 

 

 

85.7119

76.7808

64.3839

88

 

 

 

 

 

83.1792

69.9825

90

 

 

 

 

 

 

75.981

 

 

 

1.8 To find number of moles
Formula: a
Symbol:
Volume =  volume of substance in composition (m3) (note: the volume are based on unit of 1m3,  but it does not mean that the volume of the substance is 1m3)
Density: Density of the substance (kg/m3)
Molar mass-1=  Molar mass inverse (kmol/kg)

Sample Calculation for Ethanol 1:0 mixture
Volume of Ethanol:                   1m3
Density of Ethanol:     785.05kg/m3
Molar mass of Ethanol: 1kmol/46.07kg
a
a
a

Table 8: Moles of substance in different Mixture Composition


Composition
(Volume of Ethanol: Volume of n-Propanol

Mole of Ethanol (kmol)

Mole of n-Propanol (kmol)

1:0

17.04

0

8:1

136.32

13.31

4:1

68.16

13.31

1:1

17.04

13.31

1:4

17.04

53.24

1:8

17.04

106.48

0:1

0

13.31

 

 

 

1.8 To find mole fraction
Formula: a
Symbol:
Moles of substance  =    mole of a substance (kmol)
Moles of Composition = nethanol + nn-Propanol (kmol)

 

Table 9: Mole Fraction of different Mixture Composition


Composition
(Volume of Ethanol: Volume of n-Propanol

Mole fraction of Ethanol

Mole Fraction of n-Propanol

1:0

1

0

8:1

0.911047

0.088953

4:1

0.836627

0.163373

1:1

0.56145

0.43855

1:4

0.242459

0.757541

1:8

0.137953

0.862047

0:1

0

1

 

 
 
 
    
          Copyright of Gmecha 2003