Boyle's Law & Charles' Law

Test yourself

Investigation of Boyle's Law

Boyle’s Law describes the relationship between the pressure and volume of a fixed mass of gas at constant temperature.

Manometer method

Use a pump to change the air pressure on one side of the manometer.
Use a pressure gauge on the pump side to measure air pressure, which is equal to the pressure of the air in the glass tube.
You can measure the volume of trapped air.
Record the volume for several different pressure values.

Analysis of manometer method

If you plot a graph of volume against pressure, you get a monotonically decreasing curve.
Plot a graph of V^-1 against P and the best fit straight line goes through the origin.
This verifies that V^-1 is directly proportional to the pressure, i.e. pV is a constant or that P and V are inversely proportional to each other. This assumes that the temperature and mass of the gas is constant.

Further analysis of manometer method

You can use a logarithmic plot.
- Plot log(V) against log (P). It doesn’t matter what base logarithm you use.
- The gradient of the line of best fit should be -1.
Assume V = k/P where k is a constant.
- log(V) = log(k) - log(P).
- log(V) = - log(P) + log(k).

Further analysis of manometer method 2

Compare the last line with y = mx + c.
If log(V) is plotted on the y-axis, with log(P) on the x-axis, the gradient = -1 and the y-intercept should be log(k).
You can find the constant, k, using k = Z^c, where Z is the base of the logarithms (i.e. 10 or e) and c is the y-intercept.

Investigation of Boyle's Law 2

Boyle’s Law describes the relationship between the pressure and volume of a fixed mass of gas at constant temperature.

Syringe and data logging method

Connect the open end of a syringe to a pressure sensor (which is then connected to data logger and computer).
Start recording on data logger.
Move the plunger in steps, i.e. decrease or increase the volume of trapped gas slowly so as not to warm or cool the gas.
For each new volume, record the pressure.

Syringe and data logging method 2

Use software, such as a spreadsheet, to plot a graph of volume against pressure to get a monotonically decreasing curve.
Use software to plot a graph of V^-1 against P.
The best fit straight line should go through the origin, verifying that V^-1 is directly proportional to P.
- i.e. PV = constant or that P and V are inversely proportional to each other, assuming that the temperature and mass of the gas is constant.

Investigation of Charles’ Law

Charles’ Law describes the relationship between the volume and absolute temperature of a fixed mass of gas at constant pressure.

Apparatus

Set up the apparatus as shown in the diagram.
Caution: it is common practice to use a kerosene-based oil, which needed a separate risk assessment because it is available via CLEAPPS.

Method

Keep stirring the water so as to reduce temperature gradients through the water.
The length of the air column is directly proportional to the volume of trapped air. This assumes that the inner diameter of the capillary tube is constant.

Analysis

Plot a graph of the length of air column against temperature on a graph with axes as shown in the diagram.
- I.e. extended back to -400 °C so that an extrapolation back to the temperature axis can give a value for absolute zero.
Notice that the values of volume and temperature are all bunched to the right.

Analysis 2

The extrapolation is suspect because you have to extrapolate a long way before the line hits the temperature axis.
Repeating this with different gases, different volumes of gas and at different pressures gives different straight lines. All of the best fit straight lines should pass through the same point on the temperature axis.

Plot the graph again

If you plot the graph again using the student’s value for absolute zero, the length-temperature graph becomes a straight line through the origin as shown.
This shows that the volume of gas is directly proportional to the temperature in Kelvin. This assumes that the pressure and mass of the gas are constant.

1Physical Quantities & Units

1.1Physical Quantities & Units

1.1.1Use of SI Units

1.1.2SI Prefixes, Standard Form & Converting Units

1.1.3End of Topic Test - Units & Prefixes

1.1.4Avogadro's Constant

1.1.5Scalars & Vectors

2Measurement Techniques

2.1Measurement, Errors & Uncertainty

2.1.1Measuring Length, Time & Volume

2.1.2Measuring Temperature

2.1.3Circuit Measurements

2.1.4Limitation of Physical Measurements

2.1.5Uncertainty

2.1.6Estimation

2.1.7Displaying Data

2.1.8End of Topic Test - Measurements & Errors

3Kinematics

3.1Equations of Motion

3.1.1Motion in a Straight Line

3.1.2Graphs of Motion

3.1.3Bouncing Ball Example

3.1.4End of Topic Test - Motion in a Straight Line

3.1.5Acceleration Due to Gravity

4Dynamics

4.1Momentum & Newton's Laws of Motion

4.1.1Mass & Inertia

4.1.2Newton's Laws

4.1.3Momentum

4.1.4End of Topic Test - Newton's Laws & Momentum

4.1.5A-A* (AO3/4) - Newton's Third Law

4.2Non-Uniform Motion

4.2.1Projectile Motion

4.3Linear Momentum & Conservation

4.3.1Conservation of Momentum

4.4Force, Density & Pressure

4.4.1Fields

4.4.2Force in Uniform Fields

4.4.3Friction

4.4.4Buoyancy

4.4.5Terminal Speed

4.4.6End of Topic Test - Acceleration Due to Gravity

4.4.7Centre of Mass

4.4.8Forces & Equilibrium

4.4.9End of Topic Test - Scalars & Vectors

4.4.10Moments

4.4.11End of Topic Test - Moments & Centre of Mass

4.4.12Density

4.4.13Pressure

4.5Work, Energy & Power

4.5.1Work & Energy

4.5.2Power & Efficiency

4.5.3Conservation of Energy

4.5.4End of Topic Test - Work, Energy & Power

4.6Circular Motion

4.6.1Circular Motion

4.6.2Circular Motion 2

4.6.3End of Topic Test - Circular Motion

5Gravitational Fields

5.1Gravitational Fields (A2 only)

5.1.1Newton's Law

5.1.2Gravitational Field Strength

5.1.3Gravitational Potential

6Deformation of Solids

6.1Materials

6.1.1Bulk Properties of Solids

6.1.2Energy in Materials

6.1.3Young Modulus

6.1.4End of Topic Test - Materials

7Thermal Physics

7.1Thermal Physics

7.1.1Temperature

7.1.2Measuring Temperature

7.1.3Ideal Gas Law

7.1.4Ideal Gases

7.1.5Boyle's Law & Charles' Law

7.1.6Molecular Kinetic Theory Model

7.1.7Molecular Kinetic Theory Model 2

7.1.8Thermal Energy Transfer

7.1.9Thermal Energy Transfer Experiments

7.1.10End of Topic Test - Thermal Energy & Ideal Gases

7.1.11First Law of Thermodynamics

8Oscillations

8.1Simple Harmonic Motion

8.1.1Simple Harmonic Motion

8.1.2Simple Harmonic Systems

8.1.3Energy in Simple Harmonic Motion

8.1.4Resonance

8.1.5End of Topic Test - Simple Harmonic Motion

8.1.6A-A* (AO3/4) - Simple Harmonic Motion

8.1.7End of Topic Test - Gravitational Fields

8.2Waves

8.2.1Progressive Waves

8.2.2Intensity of Waves

8.2.3Wave Speed & Phase Difference

8.2.4Longitudinal & Transverse Waves

8.2.5End of Topic Test - Progressive Waves

8.2.6Electromagnetic Waves

8.2.7Doppler Effect

8.2.8Sound Waves

8.2.9Measuring Sound Waves

8.2.10End of Topic Test - Waves

8.2.11Ultrasound Imaging

8.2.12Ultrasound Imaging 2

8.3Superposition

8.3.1Stationary Waves

8.3.2Stationary Waves 2

8.3.3End of Topic Test - Stationary Waves

8.3.4A-A* (AO3/4) - Stationary Waves

8.3.5Interference

8.3.6Interference 2

8.3.7End of Topic Test - Interference

8.3.8Diffraction

8.3.9Diffraction Gratings

8.3.10End of Topic Test - Diffraction

9Communication

9.1Communication Channels

9.1.1Communication Channels

9.1.2Modulation

9.1.3Attenuation

9.2Digital Communication

9.2.1Digital & Analogue Signals

9.2.2Representing Sound

10Electric Fields

10.1Electric Fields

10.1.1Coulomb's Law

10.1.2Electric Field Strength

10.1.3Electric Field Strength 2

10.1.4Electric Potential

10.1.5End of Topic Test - Electric Fields

10.1.6A-A* (AO3/4) - Electric and Gravitational Field

10.2Capacitance

10.2.1Capacitance

10.2.2Parallel Plate Capacitor

10.2.3Energy Stored by a Capacitor

10.2.4Capacitor Discharge

10.2.5Capacitor Charge

11Current Electricity

11.1Current Electricity

11.1.1Basics of Electricity

11.1.2Mean Drift Velocity

11.1.3Current-Voltage Characteristics

11.1.4End of Topic Test - Basics of Electricity

11.1.5Resistivity

11.1.6End of Topic Test - Resistivity & Superconductors

11.1.7Power and Conservation

11.1.8Microphones

11.1.9Components

11.1.10Relays

11.1.11Strain Gauges

11.2DC Circuits

11.2.1Circuits

11.2.2Potential Divider

11.2.3Emf & Internal Resistance

11.2.4End of Topic Test - Power & Potential

12Magnetic Fields

12.1Magnetic Fields

12.1.1Magnetic Flux Density

12.1.2End of Topic Test - Capacitance & Flux Density

12.1.3Moving Charges in a Magnetic Field

12.1.4Magnetic Flux & Flux Linkage

12.1.5Electromagnetic Induction

12.1.6Electromagnetic Induction 2

12.1.7Magnetic Flux Density

12.1.8Magnetic Resonance Scanning

12.2Alternating Currents

12.2.1Alternating Currents

12.2.2Operation of a Transformer

12.2.3End of Topic Test - Electromagnetic Induction & AC

12.2.4Rectification

13Modern Physics

13.1Quantum Physics

13.1.1The Photoelectric Effect

13.1.2The Photoelectric Effect Explanation

13.1.3End of Topic Test - The Photoelectric Effect

13.1.4Collisions of Electrons with Atoms

13.1.5Energy Levels & Photon Emission

13.1.6Wave-Particle Duality

13.1.7End of Topic Test - Absorption & Emission

13.1.8Band Theory

13.1.9Diagnostic X-Rays

13.1.10X-Ray Image Processing

13.1.11Absorption of X-Rays

13.1.12CT Scanners

13.2Nuclear Physics

13.2.1Rutherford Scattering

13.2.2Atomic Model

13.2.3Isotopes

13.2.4Stable & Unstable Nuclei

13.2.5A-A* (AO3/4) - Stable & Unstable Nuclei

13.2.6Alpha & Beta Radiation

13.2.7Gamma Radiation

13.2.8Particles, Antiparticles & Photons

13.2.9Quarks & Antiquarks

13.2.10Particle Interactions

13.2.11Radioactive Decay

13.2.12Half Life

13.2.13End of Topic Test - Radioactivity

13.2.14Nuclear Instability

13.2.15Mass & Energy

13.2.16Binding Energy

13.2.17A-A* (AO3/4) - Nuclear Fusion

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