boyle's law

Experiment 3 TITLE: Boyle’s Law 3.1

INTRODUCTION

Gases have various properties which can be observed with our senses including its pressure, temperature, mass, and the volume which contains the gas. Careful, scientific observation has determined that these variables are related to one another and that the values of these properties determine the state of the gas. In the mid 1600’s, Robert Boyle studied the relationship between the pressure, p, and the volume, V, of a confined gas held at a constant temperature. Boyle’s Law states that : “ For a fixed mass of ideal gas at fixed temperature, the product of pressure and volume is a constant ” Mathematical-wise: p × V = const.

(T = const.)

Where: p is the pressure of the gas, and V is the volume of the gas A further relationship is described by the Gay-Lussac Law. This law states that if a fixed quantity of gas is contained in a constant volume, the pressure is proportional to the absolute temperature. pαT

(V = const.)

The combination of both laws leads to the general gas equation:

p1V 1 T1

=

p2V 2 T2

= const.

For a fixed quantity of gas, the expression

( p ×V ) T

always remains constant.

3.2

APPLICATION

There are several ways to alter the pressure inside any closed space. Air compressors use a piston and a valve to force additional air into the tank without allowing air to escape, but the tank always maintains its size. When we use a speaker to pressurize the air inside a cavity, like the space within a car, we pressurize the air according to Boyle’s Law. When the speaker cone moves forward (into the cavity) the pressure increases as the cavity volume decreases. The amount of the pressure change depends upon the amount of air the woofers can displace. The distance the cone moves forward times the area of the cone determines the displacement of the speaker. So, how does this relate to pressurizing the cab of a car’ Obviously, and from Boyle’s Law, the greater the reduction in volume, the greater the increase in pressure. The action of syringe. When we draw fluids into a syringe, we increase the volume inside the syringe, this correspondingly decreases the pressure on the inside where the pressure on the outside of the syringe is greater and forces fluid into the syringe. The action of the diaphragm of our body. When we inhale the diaphragm moves downward allowing the lungs an increased volume. This decreases the pressure inside the lungs so that the pressure is less than the outer pressure. This results in forcing air into the lungs. When we exhale the diaphragm moves upward and decreases the volume of the lungs. This increases the pressure inside the lungs above the pressure on the outside of the lungs so that gases are forced out of the lungs.

3.3

APPARATUS

Figure 1 shows the Boyle’s Law demonstration unit used in this experiment.

Temperature reading for Isothermic Process

Temperature reading for Isochoric Process

Pressure reading for Isochoric Process Pressure reading for Isothermic Process Heater Switch

Volume reading for Isothermic Process

Compressor Switch

Figure 1

3.4

PROCEDURE OF THE EXPERIMENTS

3.4.1 Isochoric Heating 1) Unit at master switch was switched on. 2) Air discharge valve on the lid of the heatable cylinder was opened and the vessel to ambient 3) 4) 5) 6) 7)

pressure was set. The air discharge valve was closed. The required final temperature on the heating regulator was set using the arrow keys. The heater was switched on and it is operated until final temperature is reached. Readings of temperature and pressure at equal time intervals was took until final temperature. The cylinder was leaved unchanged and was continued with cooling experiment.

3.4.2 Isochoric Cooling 1) Heater was switched off. 2) Air discharge valve on the lid of heatable cylinder was opened and vessel to ambient pressure was set. 3) Air discharge valve was closed again. 4) Readings of the temperature and pressure was took at equal intervals while vessel cools to ambient temperature. 5) Air discharge valve on the lid of the cylinder was opened and vessel to ambient pressure was set. 6) The unit at the master switch was switched off.

3.4.3 Isothermic Compression 1) Unit at the master switch was switched on.

2) Air discharge valve on the lid of the cylinder was opened halfway. 3) Both 3-way valve was placed in position 1. 4) The compressor was switched on using switch until liquid level has reached lowest mark on the scale on the cylinder. 5) The compressor was switched off. 6) Air discharge valve on the lid of the cylinder was closed. 7) The compressor was switched on. Liquid was entering the cylinder. Readings of the pressure and volume of air inside the cylinder was took as the cylinder was filled-up with the liquid. 8) The compressor was stopped once the liquid was filled-up to the upper most mark on cylinder. 9) The cylinder was leaved unchanged and was continued with the expansion experiment.

3.4.4 Isothermic Expansion 1) The air discharge valve and the 3-way valve was opened and closed interchangeably until ambient pressure was reached in the cylinder. The level of liquid in the cylinder at this time was adjusted to be at the upper mark of the cylinder. 2) The air discharge valve was closed. 3) The compressor was switched on and the gas volume was expanded until the lowest mark on the scale of the cylinder was reached. The readings of the pressure and volume of the air was took throughout this process at regular intervals.

3.5

RESULTS

3.5.1

Isochoric Heating and Cooling

Heating No. 1

Time, t (min) 1

Temperature, T ( C) 22.3

Pressure, p (bar) 1.06

2

2

28.5

1.12

3

3

37.9

1.18

p (bar) / T (K) 3.59 ×

10−3

3.71 ×

10

3.80 ×

10−3

−3

4

4

49.2

1.22

5

5

61.5

1.26

6

6

71.9

1.27

7

7

79.5

1.27

No 1

Time, t (min) 1

Temperature, T ( C) 85.4

Pressure, p (bar) 0.99

2

2

84.4

0.97

3

3

82.9

0.96

4

4

80.8

0.95

5

5

78.5

0.95

6

6

76.0

0.94

7

7

73.2

0.93

8

8

70.8

0.92

9

9

68.1

0.92

10

10

65.6

0.91

11

11

63.3

0.91

12

12

61.1

0.90

13

13

58.9

0.90

14

14

57.0

0.89

15

15

55.1

0.89

3.79 ×

10−3

3.77 ×

10−3

3.68 ×

10−3

3.60 ×

10−3

Cooling

3.5.2

p (bar) / T (K) 2.76 ×

10−3

2.71 ×

10−3

2.70 ×

10

2.69 ×

10−3

2.70 ×

10

2.69 ×

10−3

2.69 ×

10−3

2.68 ×

10

2.70 ×

10−3

2.69 ×

10

2.71 ×

10−3

2.69×

10−3

2.71 ×

10−3

2.70 ×

10−3

2.71 ×

10

Isothermic Compression and Expansion

Compression NO

Volume, V ( m

3

)

Pressure, p (bar)

p × V (Nm)

−3

−3

−3

−3

−3

. 1 2 3 4 5

2.76 2.31 1.76 1.23 0.67

1.08 1.29 1.61 2.17 3.25

298080 297990 283360 266910 217750

Pressure, p (bar)

p × V (Nm)

0.79 0.54 0.41 0.33 0.27

47400 62100 69700 74910 73980

Expansion No. 1 2 3 4 5

Volume, V ( m 0.60 1.15 1.70 2.27 2.74

Isochoric Heating

3

)

Pressure, P against Temperature, T 1.3 1.25 1.2 1.15 Pressure, P

1.1 1.05 1 0.95 10

20

30

40

50

60

70

80

90

Temperature, T

Pressure Over Temperature, P/T against time, t 0 0 0 0 P/T

0 0 0 0 0 0

1

2

3

4 Time, t

5

6

7

8

Isochoric cooling

Pressure, P against Temperature, T 1 0.98 0.96 0.94 0.92

Pressure, P

0.9 0.88 0.86 0.84 50

55

60

65

70

75

80

85

90

Temperature, T

Pressure over Temperature, P/T against Time,t 0 0 0 0 P/T 0 0 0 0 0

2

4

6

8 Time, t

10

12

14

16

Isothermic compression

Pressure, P Against Volume, V 3.5 3 2.5 2 Pressure, P

1.5 1 0.5 0 0.5

1

1.5

2

2.5

3

Volume, V

Isothermic Expansion

Pressure, P against Volume, V 0.9 0.8 0.7 0.6 0.5 Pressure, P

0.4 0.3 0.2 0.1 0 0

0.5

1

1.5 Volume, V

2

2.5

3

3.6

REFERENCES 1. Thermodynamics, An Engineering Approach (7th Edition) SI Version, Yunus A. Cengel; Michael A. Boles. McGraw Hill. 2. Fundamentals of Thermodynamics(7th Edition) SI Version, Claus Borgnakke; Richard E. Sonntag. Wiley Publications 3. Principles of Engineering Thermodynamics (7th Edition) SI Edition, Michael J. Moran; Howard N. Shapiro; Daisie D. Boettner; Margaret B. Bailey. Wiley Publications.