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In an experiment to verify Boyle’s law, a student measured the length of a column of air of fixed mass and uniform diameter, at different values of air pressure p - Leaving Cert Physics - Question 2 - 2022

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In an experiment to verify Boyle’s law, a student measured the length of a column of air of fixed mass and uniform diameter, at different values of air pressure p. ... show full transcript

Worked Solution & Example Answer:In an experiment to verify Boyle’s law, a student measured the length of a column of air of fixed mass and uniform diameter, at different values of air pressure p - Leaving Cert Physics - Question 2 - 2022

Step 1

State Boyle's law.

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Answer

Boyle's law states that the pressure of a fixed mass of gas is inversely proportional to its volume at constant temperature. This can be expressed mathematically as:

PimesV=kP imes V = k

where P is the pressure, V is the volume, and k is a constant.

Step 2

Draw a labelled diagram of how the apparatus was arranged in this experiment.

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Answer

The apparatus should include:

  1. A glass tube with a uniform diameter, filled with air.
  2. A manometer or pressure gauge for measuring the pressure of the air column.
  3. A ruler or measurement device to measure the length of the air column in centimeters.
  4. Supports to hold the apparatus upright.
  5. Labels for each component: 'Glass Tube', 'Pressure Gauge', 'Air Column Length'.

Step 3

Why is it necessary for the column of air to have a uniform diameter?

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Answer

A uniform diameter is necessary to ensure that the relationship between pressure and volume is consistent throughout the column. Variability in diameter could create areas of differing pressure or volume, thereby leading to erroneous interpretations of Boyle's law.

Step 4

Draw a suitable graph to verify Boyle's law.

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Answer

To verify Boyle's law, plot volume (1/p) against pressure (P).

The pressure values (p) should be converted to their corresponding volume values using the data collected:

  1. Create a new table with columns for 1/p (in kPa) and corresponding lengths (in cm).
  2. The graph will typically be a straight line through the origin, demonstrating the inverse relationship.

Step 5

Explain how your graph verifies Boyle's law.

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Answer

The graph demonstrates that as the pressure increases, the volume (length of the air column) decreases, which is consistent with Boyle's law. The linearity of the graph confirms the inverse relationship, where the product of pressure and volume remains constant.

Step 6

Which of the data points is inconsistent with the others?

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Answer

The inconsistent data point is when l = 20.0 cm and p = 227 kPa. This point does not align with the expected trend of the graph, contradicting the proportional relationship expected from Boyle's law.

Step 7

How did you treat this data point when you drew your graph?

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Answer

This data point was disregarded when constructing the graph. By omitting this outlier, the integrity of the relationship between pressure and volume is maintained, providing a clearer representation of Boyle's law.

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