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# Investigating the relationship between pressure, volume and temperature of a gas

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Introduction

Title

Investigating the relationship between pressure, volume and temperature of a gas

Objective

• To investigate, for a fixed amount of gas, the relationship between
• volume and temperature at constant pressure, i.e. Charles’s law
• pressure and temperature at constant volume, i.e. Pressure law
• pressure and volume at constant temperature, i.e. Boyle’s law

Apparatus

Capillary tube (with silver thread)        x1                 Thermometer                                        x1

500 mL round-bottomed flask           x1                Bourdon gauge                                x1

100 mL syringe                                x1            Hot plate with magnetic stirrer        x1

2500 mL beaker                                x1                Jack                                                        x1

Theory

Thermal behavior of gases is often described by sets of relationship among the common macroscopic quantities such as pressure P, volume V, temperature T and mass m. In this experiment, fixed amount of air is used as the gas for investigation. Since only two variables should be changed at one time, consequently there are three relationships to be explored: (I) V-T at constant P, (II) P-T at constant V, and (III) P-V at constant T.

(I) V-T at constant P

To establish a constant pressure environment while allowing volume and temperature to change, a small amount of air is trapped under a mercury thread in a capillary tube (uniform bore diameter) with the lower end closed and the upper end open to atmosphere. The capillary tube is immersed in a water bath of variable temperature.

Middle

3. The piston was pulled slowly to increase the volume of air inside the syringe to a convenient value according to the syringe’s scale. The Bourdon gauge was tapped lightly before taking the same set of readings. The results were tabulated.

4. Step 3 was repeated until the piston could not be pulled further. However, excessive force must be avoided as it might damage the syringe. The initial volume was reached finally.

5. The piston was pushed slowly to decrease the volume of air inside the syringe to a convenient value according to the syringe’s scale. The results were tabulated.

6. Step 5 was repeated until the piston could not be pushed further. However, excessive force must be avoided as it might damage the syringe. The initial volume was reached finally.

Results

(I)V-T at constant P and (II) P-T at constant V

The temperature, the length of the air column and the pressure of the air inside the round-bottomed flask were tabulated in the table below:

 Temperature (I) V–T at constant P (ii) P–T at constant V T / °C Length of air column h / cm Pressure of air P / 100 kPa 30 6.1 1 46 6.5 1.025 51 7.0 1.050 65 7.5 1.075 72 7.7 1.100 80 7.9 1.125 85 8.1 1.150 96 8.5 1.175

The graph of h against T was plotted below: From the equation y = 0.0369x + 4.9935,

when y = 0, x-intercept = -4.9935/ 0.0369 = -135oC

The graph of P against T was plotted below: Conclusion

V is difficult to measure. When the straight line is extrapolated, it cuts T-axis at -135oC, which is far away from the expected result of -273 oC. However, by allowing the experimental errors, the volume of air V is still directly proportional to the temperature T measrued in K at constant pressure P, i.e. the results obey Charles’ law.

In experiment (II), the slope of the graph depends on the number of moles of air n and the volume of air V by the equation PV = nRT. When the straight line is extrapolated, it cuts T-axis at -336oC, which is away from the expected result of -273 oC. However, by allowing the experimental errors, the pressure of air P is still directly proportional to the temperature T measrued in K at constant volume V, i.e. the results obey Pressure law.

In experiment (III), the graph of P against 1/ V is plotted instead of the graph of P against V because the line in the graph of P against V is a hyberbola which has no physical meaning for analysis. From the graph, the straight line passes the origin, indicating that the pressure of air P is directly proportional to 1/ the volume of air 1/ V. In other words, the pressure of air P is inversely proportional to the volume of air V at constant temperature T, i.e. the results obey Boyle’s law.

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