1B40

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1B40 1B28 CP/CV for an Ideal GasNeal
Skipper (n.skipper_at_ucl.ac.uk)

• To provide some background to specific heats of
  gases.
• To provide an example of data collection and
  uncertainties.

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CP/CV for an Ideal Gas

• What is CP/CV ?
• How do we measure CP/CV ?
• Video clip
• Some General Principles for doing Experiments
• Application to CP/CV

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What is CP/CV ?

• The ratio of specific heats, Cp/Cv is usually
  called ?. ? is an important characteristic of a
  gas since it reflects on a macroscopic scale the
  microscopic properties of the molecules.

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What is CP/CV ?

• Cp and Cv are the molar heat capacities at
  constant pressure and constant volume
  respectively.
• CP is bigger than Cv, because at constant
  pressure the gas can do work (expanding).

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What is CP/CV ?

• CP is bigger than Cv, because at constant
  pressure the gas can do work (expanding).

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What is CP/CV ?

• Equipartition of energy tells us that
• Where s is the number of degrees of freedom of
  the particles in the gas.
• For a monatomic gas, such as Ar, s 3
  (translation in x, y and z).

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What is CP/CV ?

• For a monatomic gas, such as Ar, s 3
  (translation in x, y and z).
• So for a monatomic gas

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How do we measure CP/CV ?Oscillating Ball Method!
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How do we measure CP/CV ?Oscillating Ball Method!

• Methods for determining ? are usually based on
  adiabatic expansion and compression of the gas.
  So
• If the ball is displaced a distance x from its
  equilibrium position then the change of volume of
  the gas is

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How do we measure CP/CV ?Oscillating Ball Method!

• To a first approximation the restoring force is
  then proportional to the displacement, x.
• This is the condition for simple harmonic motion.

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How do we measure CP/CV ?Oscillating Ball Method!

• So
• and
• where ? frequency of the oscillation.

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Show Video Clip Here !!Is it safe??
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How do we measure CP/CV ?Oscillating Ball Method!

• A 197.9 ? 0.5 mm2
• M 16.432 ? 0.002 g
• V 1252 ? 5 cm3
• P 101101 ? 5 Pa
• ? ?? ? ??

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Some General Principles for Doing Experiments

• Be Safe Identify Potential Risks
• Open Notebook and Prepare to Write
• Understand and Record What it is You Want to
  Measure and Why
• Do a Preliminary Measurement

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Some General Principles for Doing Experiments

• Identify the quantity that contributes most to
  the final error try to reduce it by
• Making more measurements
• Plotting a graph
• Using a different method
• Try to avoid mistakes and systematic errors
• Estimate the quantity you are going to measure
• Be careful with units

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Some General Principles for Doing Experiments

• An estimate of the final error to around 1 part
  in 5 is usually fine
• Quote the final result and error to the same
  number of digits.

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Application to CP/CVUnits and percentage errors

• A 197.9 ? 0.5 mm2 1.97910-4m2 ? 0.3
• M 16.432 ? 0.002 g 0.016432 kg ? 0.01
• V 1252 ? 5 cm3 1.252 10-3m3 ? 0.4
• P 101101 ? 5 Pa 101101 Pa ? 0.05
• ? ?? ? ??
• So reduce error in ? and V
• Any other potential prat-falls??

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Application to CP/CVCombining errors
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Application to CP/CVMeasuring ? and
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Show Video Clip Here !!
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Application to CP/CVMeasuring ? and

• I think there are two main difficulties
• Reaction time to start stopwatch
• Keeping count
• To minimise these we can
• Plot a graph of time taken against number of
  oscillations. The gradient will give ? and the
  intercept the reaction time.
• Make a number of observations. We can then detect
  rogues (! Be careful here !) and also reduce
  standard error

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Excel File Goes Here!
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Conclusions

• We find that for argon
• Literature value is 1.67
• Possible ways to reduce uncertainties
• Electronic counting
• Possible systematic errors
• Counting/timing
• Non-adiabatic processes
• Friction as ball oscillates not harmonic motion