PHAS1240: Procedures, Notebooks, Formal Reports and Data Analysis

1
PHAS1240 Procedures, Notebooks, Formal Reports
and Data Analysis

• Dr. Neal Skipper (n.skipper_at_ucl.ac.uk)
• Dr. Christine Bull (christine.bull_at_ucl.ac.uk)

2
PHAS1240 Lectures on 23rd and 30th October 2006

• Some General Comments on Procedures
• Laboratory Notebooks
• Formal Reports
• Data Analysis an example (please bring
  stopwatch and calculator next week)

3
Data Analysis see Appendix III of Student
Handbook

• Some General Principles
• Experimental Procedures
• Minimising Experimental Uncertainties
• Summary of Uncertainties
• An example Cp/Cv for an Ideal Gas
• Bouncing Ball Experiment

4
Some General Principles Experimental Procedures

• Be sensible Safety is everyones
  responsibility.
• Keep a record in your notebook as you go along.
• Read any instructions try to plan what you are
  going to do.
• Understand and Record What it is You Want to
  Measure and Why.
• Do a Preliminary Measurement if Necessary.

5
Cp/Cv The MovieShow Video Clip Here !!
6
Some General PrinciplesMinimising Experimental
Uncertainties

• Avoid mistakes
• Estimate the quantity you are going to measure
• Be careful with units
• Identify any possible systematic errors
• Identify the quantities that contribute most to
  the final error try to reduce them by
• Making more measurements
• Plotting a graph
• Using a different (very cunning) method

7
Some General PrinciplesSummary of Uncertainties

• Errors
• Random errors (uncertainties) are variable and
  mainly affect precision
• Systematic errors are usually constant and mainly
  affect accuracy.
• Quote errors to same number of figures as the
  quantity itself, for example
• g 9.55?0.05 ms-2
• An estimate of the final error to around 1 part
  in 5 is usually fine

8
Some General PrinciplesMinimising Experimental
Uncertainties

• You can ignore all errors whose contribution to
  the total final error is less than about a fifth
  of the largest contribution.

9
Some General PrinciplesSummary of Uncertainties

• Sets of Measurements
• Mean value of the sample
• ith residual
• Standard deviation of the sample
• Gaussian or normal distribution
• Standard error (deviation) on the mean of the
  distribution

10
Some General PrinciplesSummary of Uncertainties

• Combining Uncertainties

11
An ExampleMeasuring Cp/Cv for an Ideal Gas

• 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).

12
An Example Cp/Cv for an Ideal Gas

• 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.

13
How do we measure CP/CV Oscillating Ball Method
14
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,
  where ? frequency of the oscillation

15
How do we measure CP/CV Oscillating Ball Method

• 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
• ? ?? ? ??

16
How do we measure CP/CV Combining errors
17
Cp/Cv The MovieShow Video Clip Here !!
18
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

19
My working in Excel