##### Document Text Contents

Page 3

3

where

ω’= √

. (12)

The above relation can be expressed as :

1/T

2

=( γPatmA +mg / 4π

2

my0) – b

2

/16π

2

m

2

(13)

Where T= 2π/ω’ is the period of the damped oscillation, or the time interval between two

successive peaks.

II. Methodology

To begin the experiment, the materials and equipment needed were a Pasco heat engine

apparatus and a Vernier LabPro with gas pressure sensor. The instruments were set up with care

before experimental data were gathered. The diameter of the piston used was 32.5mm or

0.0325m and the mass of the platform of the piston was 35g or 0.035kg.

When the instruments have been set up, the piston was put at a height of 0.075m and

tightened. Then, the LabPro started collecting data as the piston was lightly tapped. By zooming

in the graph of the pressure versus time graph in the LabPro, the period was recorded. To ensure

that one whole period is measured, the peaks of the graphs were taken account. This process is

done for heights of 0.080m, 0.085m, .0.090m and 0.095m of the piston.

Data were then input on Microsoft Excel. The data was plotted by the computer program

and the linearly fit. The equation of the best fit line was then recorded. The specific heat ratio

was then calculated.

III. Results and Discussion

The measured periods can be found in Table W2 as the height of the piston varies.

Height of Piston (m) Period (s)

0.075 0.032

0.080 0.034

0.085 0.036

0.090 0.038

0.095 0.04

Table W2. Measured Data

The calculated reciprocal of the height of the piston y

-1

and the calculated reciprocal of

the square of the period T

-2

can be found in Table W2.1.

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4

y-1 T-2

13 976

12 865

11 771

11 692

10 625

Table W2.1. T-2 and y-1 Data

The graph of the reciprocal of the height of the piston y

-1

and the reciprocal of the square

of the period T

-2

can be found in Figure W2.

Figure W2. T-2 vs y-1 Graph

From the graph of the reciprocal of the height of the piston y

-1

and the reciprocal of the

square of the period T

-2

, the best fit line is found to be y = 119.31x - 574.31

From equation (11) the specific heat ratio is computed from the slope of the best fit line.

γ = [ (slope)(4π

2

m) –mg ]/ PatmA (12)

The experimental specific heat ratio and percent deviation from the theoretical heat ratio

of 7/5 or 1.4 is given in Table W3.

Experimental Specific

Heat Ratio

Percent Deviation

1.96 40%

Table W3. Specific Heat Ratio

y = 119.31x - 574.31

0

200

400

600

800

1000

1200

0 5 10 15

T-2

y-1

T-2 vs y-1

3

where

ω’= √

. (12)

The above relation can be expressed as :

1/T

2

=( γPatmA +mg / 4π

2

my0) – b

2

/16π

2

m

2

(13)

Where T= 2π/ω’ is the period of the damped oscillation, or the time interval between two

successive peaks.

II. Methodology

To begin the experiment, the materials and equipment needed were a Pasco heat engine

apparatus and a Vernier LabPro with gas pressure sensor. The instruments were set up with care

before experimental data were gathered. The diameter of the piston used was 32.5mm or

0.0325m and the mass of the platform of the piston was 35g or 0.035kg.

When the instruments have been set up, the piston was put at a height of 0.075m and

tightened. Then, the LabPro started collecting data as the piston was lightly tapped. By zooming

in the graph of the pressure versus time graph in the LabPro, the period was recorded. To ensure

that one whole period is measured, the peaks of the graphs were taken account. This process is

done for heights of 0.080m, 0.085m, .0.090m and 0.095m of the piston.

Data were then input on Microsoft Excel. The data was plotted by the computer program

and the linearly fit. The equation of the best fit line was then recorded. The specific heat ratio

was then calculated.

III. Results and Discussion

The measured periods can be found in Table W2 as the height of the piston varies.

Height of Piston (m) Period (s)

0.075 0.032

0.080 0.034

0.085 0.036

0.090 0.038

0.095 0.04

Table W2. Measured Data

The calculated reciprocal of the height of the piston y

-1

and the calculated reciprocal of

the square of the period T

-2

can be found in Table W2.1.

Page 4

4

y-1 T-2

13 976

12 865

11 771

11 692

10 625

Table W2.1. T-2 and y-1 Data

The graph of the reciprocal of the height of the piston y

-1

and the reciprocal of the square

of the period T

-2

can be found in Figure W2.

Figure W2. T-2 vs y-1 Graph

From the graph of the reciprocal of the height of the piston y

-1

and the reciprocal of the

square of the period T

-2

, the best fit line is found to be y = 119.31x - 574.31

From equation (11) the specific heat ratio is computed from the slope of the best fit line.

γ = [ (slope)(4π

2

m) –mg ]/ PatmA (12)

The experimental specific heat ratio and percent deviation from the theoretical heat ratio

of 7/5 or 1.4 is given in Table W3.

Experimental Specific

Heat Ratio

Percent Deviation

1.96 40%

Table W3. Specific Heat Ratio

y = 119.31x - 574.31

0

200

400

600

800

1000

1200

0 5 10 15

T-2

y-1

T-2 vs y-1