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In an experiment to verify Boyle's law, a student measured the volume $V$ of a fixed mass of gas at different values of the pressure $p$ - Leaving Cert Physics - Question 1 - 2015
Question 1
In an experiment to verify Boyle's law, a student measured the volume $V$ of a fixed mass of gas at different values of the pressure $p$. The temperature of the gas ... show full transcript
Worked Solution & Example Answer:In an experiment to verify Boyle's law, a student measured the volume $V$ of a fixed mass of gas at different values of the pressure $p$ - Leaving Cert Physics - Question 1 - 2015
Step 1
Describe, with the aid of a labelled diagram, how the student obtained the data.
Answer
The student conducted the experiment using a gas column in a vertical setup, where the gas was contained in a closed environment. The apparatus included a volume scale along the marked column, a pressure gauge to measure the corresponding pressure, and a mechanism to change the volume by adjusting the piston. The following steps were taken:
- Set up the apparatus: The gas column was filled with air and allowed to stabilize.
- Measure initial volume: The volume was recorded as indicated on the scale for each pressure reading.
- Adjust pressure: The gas was compressed or expanded using the piston. The pressure was noted from the gauge after each adjustment.
- Repeat measurements: The process was repeated at various fixed volumes to obtain corresponding pressure values, ensuring multiple readings for accuracy.
Step 2
Draw a suitable graph to show the relationship between the pressure of the gas and its volume.
Answer
To illustrate the relationship between pressure and volume:
- X-axis: Volume (cm³)
- Y-axis: Pressure (kPa)
- Data points: Plot the points from the recorded data.
- Graph Type: A straight line should be drawn, which reflects the inverse relationship evident in Boyle's law. The graph should show a downward curve indicating that as volume increases, pressure decreases.
Step 3
Explain how the graph verifies Boyle's law.
Answer
Boyle's law states that for a fixed amount of gas at constant temperature, the pressure is inversely proportional to the volume. This relationship can be mathematically expressed as: Here, is pressure, is volume, and is a constant. From the graph, as the volume increases, the pressure decreases, maintaining the product constant across various points on the graph. This supports Boyle's law and demonstrates the expected inverse relationship.
Step 4
Use your graph to estimate the pressure of the gas at a volume of 250 cm³.
Answer
From the graph, to find the pressure at a volume of 250 cm³, locate this volume on the X-axis and draw a vertical line to intersect the curve. The intersection point with the Y-axis will give the estimated pressure value. Based on visual extrapolation, the pressure at 250 cm³ can be estimated to be approximately 105 kPa.
Step 5
Why might the temperature of the gas have changed significantly during the experiment?
Answer
The temperature of the gas could change significantly due to:
- Compression or expansion work: Increasing pressure compresses the gas, which can generate heat, raising its temperature.
- Environmental factors: Fluctuations in the surrounding temperature during measurements may also contribute to changes in gas temperature.
Step 6
How did the student ensure that the temperature of the gas was the same for each measurement?
Answer
To maintain the same temperature throughout the experiment, the student:
- Made sure to wait long enough after each adjustment of the piston to allow the gas to reach thermal equilibrium with the surroundings.
- Ensured that any changes in volume were made slowly to minimize the generation of heat due to rapid compression or expansion. This careful handling helped ensure consistent temperature for all measurements.