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Thermal Physics | Practical No 23A - Verifying Boyle's law | A/L Physics Practical

DP Education - A/L සිංහල මාධ්‍යය・51 minutes read

Boyle's Law demonstrates the inverse relationship between the pressure and volume of a gas at constant temperature, verified through experiments using specialized apparatus to measure mercury levels and gas volumes. The collected data is used to plot graphs that confirm the law, allowing calculations of atmospheric pressure and reinforcing the principle that pressure increases as volume decreases.

Insights

  • Boyle's Law describes the fundamental relationship between the pressure and volume of a gas, stating that when temperature and mass remain constant, an increase in pressure leads to a decrease in volume, which can be mathematically expressed as PV = k, highlighting the inverse relationship that is central to understanding gas behavior.
  • The experiment to demonstrate Boyle's Law involves using Boyle's apparatus, which consists of two glass tubes connected by a rubber tube, where adjustments to the height of the open tube affect the mercury level, allowing for direct observation of how pressure changes correlate with volume reduction in the trapped gas.
  • Accurate data collection is crucial for verifying Boyle's Law; the experiment requires at least five measurements of mercury heights to ensure reliable readings, and the resulting data is plotted on a graph with height versus the inverse of volume, where a straight line indicates successful verification of the law.
  • The experiment also provides a method for calculating atmospheric pressure using the intercept and gradient from the plotted graph, illustrating how experimental data can be used not only to confirm theoretical principles but also to derive important physical constants like atmospheric pressure.

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Recent questions

  • What is Boyle's Law?

    Boyle's Law is a fundamental principle in physics that describes the relationship between the pressure and volume of a gas. It states that for a given mass of gas at constant temperature, the pressure exerted by the gas is inversely proportional to its volume. This means that if the volume of the gas decreases, the pressure increases, and vice versa. Mathematically, this relationship is expressed as PV = k, where P represents pressure, V represents volume, and k is a constant. Boyle's Law is crucial for understanding gas behavior in various scientific and practical applications, such as in the fields of chemistry, physics, and engineering.

  • How to conduct Boyle's Law experiment?

    Conducting an experiment to verify Boyle's Law involves using Boyle's apparatus, which typically consists of two glass tubes connected by a rubber tube, with one end closed and the other open. To begin, set up the apparatus vertically, ensuring the closed-end tube is positioned centrally for accurate readings. Fill the apparatus with a trapped mass of gas and mercury, then adjust the height of the open-ended tube to create different pressure conditions. Take at least five readings of the mercury levels, recording the height difference (h) and the corresponding volume of the gas. After collecting the data, plot a graph with 1/L (inverse of length) on the y-axis and h (height) on the x-axis. A straight line on the graph will confirm the inverse relationship between pressure and volume, thus verifying Boyle's Law.

  • What is atmospheric pressure?

    Atmospheric pressure is the force exerted by the weight of the air above a given point on the Earth's surface. It is typically measured in units such as pascals (Pa), millibars (mb), or inches of mercury (inHg). At sea level, the average atmospheric pressure is approximately 101,325 Pa or 1013.25 mb. Atmospheric pressure plays a significant role in various natural phenomena, including weather patterns and the behavior of gases. In experiments involving gases, such as those verifying Boyle's Law, atmospheric pressure is a critical factor as it influences the pressure exerted by the gas in the apparatus. Understanding atmospheric pressure is essential for applications in meteorology, aviation, and various scientific fields.

  • Why use mercury in experiments?

    Mercury is often used in experiments involving pressure measurement, such as those verifying Boyle's Law, due to its unique physical properties. One of the primary advantages of using mercury is its high density, which allows for significant pressure changes to be observed with relatively small height differences in the mercury column. This makes it easier to measure and interpret results accurately. Additionally, mercury has a low vapor pressure, which minimizes the risk of gas escaping into the atmosphere during experiments. Its liquid state at room temperature and ability to form a clear meniscus also facilitate precise measurements. However, due to its toxicity, safety precautions must be taken when handling mercury in laboratory settings.

  • How to calculate atmospheric pressure?

    To calculate atmospheric pressure in an experiment, you can use the relationship defined by Boyle's Law, which states that the product of pressure and volume for a gas remains constant. The formula P₁V₁ = P₂V₂ can be applied, where P₁ is the initial pressure (which includes atmospheric pressure), V₁ is the initial volume, P₂ is the pressure at a second volume, and V₂ is that second volume. By rearranging the equation, you can isolate atmospheric pressure and calculate it based on the known values of pressure and volume from your experiment. For instance, if you have measurements from a gas trapped in a piston, you can substitute the values into the equation to derive the atmospheric pressure, which is essential for understanding the behavior of gases under varying conditions.

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Summary

00:00

Verifying Boyle's Law Through Experimentation

  • Boyle's Law states that the pressure exerted by a gas is inversely proportional to its volume when the temperature and mass of the gas remain constant, expressed mathematically as PV = k, where P is pressure, V is volume, and k is a constant.
  • The experiment to verify Boyle's Law uses Boyle's apparatus, which consists of two glass tubes connected by a rubber tube, with one end closed and the other open, containing a trapped mass of gas and mercury.
  • When the open end of the apparatus is raised, the height of the mercury column increases, leading to increased pressure on the trapped gas, which in turn reduces its volume, demonstrating the inverse relationship between pressure and volume.
  • The height difference (h) between the mercury levels in the two tubes contributes to the total pressure, which is the sum of atmospheric pressure and the pressure due to the height of the mercury column.
  • The volume of the gas can be expressed as V = A × L, where A is the cross-sectional area of the tube (constant) and L is the length of the gas column, while the pressure can be expressed as P = P₀ + h, where P₀ is atmospheric pressure.
  • To conduct the experiment, the Boyle's apparatus must be set up vertically, with the closed-end tube positioned at the center to ensure accurate readings of the mercury levels.
  • A set square or triangle ruler is recommended to minimize reading errors when measuring the mercury levels, ensuring that the apparatus is viewed at eye level to avoid parallax errors.
  • The experiment involves adjusting the height of the open-ended tube to obtain at least five readings of the mercury levels, allowing for the calculation of the height difference (h) and the length of the gas column (L) at each point.
  • After collecting the data, a graph is plotted with 1/L on the y-axis and h on the x-axis; a straight line indicates that Boyle's Law is verified, and the atmospheric pressure can be calculated from the graph's intercept and gradient.
  • The primary tools required for the experiment are Boyle's apparatus and a set square or ruler, with the procedure being straightforward: adjust the height, take readings, and plot the graph to confirm the inverse relationship between pressure and volume.

19:30

Measuring Pressure with a Mercury Barometer

  • To increase or decrease pressure in a mercury barometer, adjust the height of the open-ended side, which directly affects the pressure exerted by the mercury column due to its weight.
  • The pressure measurement is determined by the height difference (h) between two mercury levels, where the height of mercury from the closed end to the open end indicates the pressure exerted on the trapped gas.
  • The relationship between pressure (h) and volume (l) is established, where h is proportional to pressure and l is proportional to volume, leading to the conclusion that pressure and volume are inversely proportional (Boyle's Law).
  • To verify Boyle's Law, a graph is plotted with pressure (h) on the y-axis and the inverse of volume (1/l) on the x-axis, which should yield a straight line through the origin if Boyle's Law holds true.
  • For accurate readings, at least five measurements should be taken: one at maximum height, one at minimum height, and three intermediate readings to minimize errors in the experiment.
  • The first set of readings includes: open-ended mercury level at 83.9 cm, closed end at 45.4 cm, resulting in h = 38.5 cm and l = 14.6 cm (60 - 45.4).
  • The second set of readings shows the open-ended level at 72.9 cm and closed end at 44 cm, yielding h = 28.9 cm and l = 16 cm (60 - 44).
  • The third set of readings records the open-ended level at 54.8 cm and closed end at 41 cm, resulting in h = 13.8 cm and l = 19 cm (60 - 41).
  • The fourth set of readings captures the open-ended level at 33.5 cm and closed end at 24.6 cm, giving h = 8.9 cm and l = 26.5 cm (60 - 33.5).
  • The final set of readings has the open-ended level at 37.2 cm and closed end at 36.1 cm, resulting in h = 1.1 cm and l = 22.8 cm (60 - 36.1), completing the five readings necessary for graphing.

39:43

Graphing Boyle's Law Experiment Results

  • The experiment involves plotting points on a graph with axes labeled as height (h) in centimeters and 1/l (inverse of length) in centimeters⁻¹, with values ranging from -10 to 40 for h and corresponding values for 1/l.
  • Specific data points to be plotted include (38.5, 0.064), (28.9, 0.063), (13.8, 0.053), (-8.9, 38), and (-1.1, 0.044), with careful attention to their precise locations on the graph.
  • A line of best fit is drawn through the plotted points, acknowledging that experimental errors may cause deviations from a perfect straight line, which is common in practical experiments.
  • The intercept of the line is identified at 0.044, and the gradient is calculated using two points, resulting in a delta y of 0.018 and a delta x of 28, leading to a gradient of approximately 0.64 × 10⁻³.
  • Atmospheric pressure is derived from the intercept and gradient using the formula: atmospheric pressure = intercept/gradient, yielding a calculated atmospheric pressure of approximately 69 centimeters of mercury.
  • The experiment verifies Boyle's Law, which states that the volume of a constant mass of gas is inversely proportional to its pressure at constant temperature.
  • A J-tube can be used as an alternative apparatus to verify Boyle's Law, allowing for temperature changes by submerging it in a hot water bath, although it lacks a scale for easy measurement.
  • Mercury is preferred over other liquids in this experiment due to its high density, which allows for significant pressure changes with small height differences, making the experiment more practical.
  • The measurements taken during the experiment include the height difference (h) of the mercury levels and the length (l) of the air column, which are crucial for calculating pressure and volume.
  • The graph plotted should have 1/l on the y-axis and h on the x-axis, as h is the independent variable that is manipulated, while 1/l is the dependent variable that changes accordingly.

01:03:47

Measuring Atmospheric Pressure with Boyle's Law

  • In the experiment, a plastic cylinder with a tight piston traps air, and the bottom end is sealed to prevent airflow, allowing for pressure measurement when the piston is pushed downwards, compressing the trapped air.
  • The pressure exerted on the trapped air can be calculated using the formula: Pressure (P) = Atmospheric Pressure (P₀) + (Force (F) / Area (A)), where Force is derived from the balance reading (mass in kg multiplied by gravitational acceleration, typically 10 m/s²).
  • When the piston is pushed to two different positions, the volume of trapped air is recorded as 18 mL and 10 mL, with corresponding balance readings of 0.6 kg and 3.6 kg, respectively, which are essential for applying Boyle's Law.
  • Boyle's Law states that the volume of a constant mass of gas is inversely proportional to its pressure at constant temperature, which is crucial for determining atmospheric pressure in this experiment.
  • To calculate atmospheric pressure using the given data, the formula P₁V₁ = P₂V₂ is applied, where P₁ is the initial pressure (P₀ + 0.6 * 10 / (4 * 10⁻⁴)), V₁ is 18 mL, and P₂ is the pressure at the second volume of 10 mL with a balance reading of 3.6 kg.
  • The calculated atmospheric pressure is approximately 7.875 × 10⁴ N/m², derived from manipulating the equations and substituting the known values for pressure and volume.
  • To find the volume of trapped air when the balance reading is zero (indicating only atmospheric pressure), the equation P₁V₁ = P₃V₃ is used, leading to a calculated volume of approximately 21.4 mL when the pressure is solely atmospheric.
  • For measuring lower pressures than atmospheric pressure, the piston can be pulled upwards, and a spring scale can be used to measure the force applied, with the setup inverted to allow for accurate readings of the force exerted while maintaining the pressure drop in the trapped air.
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