Description
Some homework problems and class exercises will use simulations developed by the text authors.
These can all be run from a java “launcher.” You should first install the launcher on the computer
that you are using. To do this:
1. Go to the following webpage: http://www.compadre.org/STP/items/detail.cfm?ID=7308.
2. Download the file called “download 3239kb.jar.” You may have to save it and then run it.
Running the file produces a “launcher” window (with the tab title Open Source Physics: osp stp.xset)
which lists a long collection of simulations for statistical and thermal physics these are sorted into
folders in the directory on the left. Double click on any entry to run the relevant simulation.
General tips about running the simulations:
1. Clicking on a simulation in the “launcher” will produce documentation for the simulation in
the launcher window.
2. The “launcher” usually opens a controller window but not necessarily the other windows
associated with the simulation. The controller window lets you set parameters. Once you
have done this clicking Initialize will open the simulation usually with some other graphical
windows. Clicking Start will actually run the simulation.
3. Graphs and images can be save by following Tools → Snapshot . . . .
4. The data that is generated by the simulation can be accessed in tabular form by following
Tools → Data Tool, selecting one of the starred objects and clicking OK. This contains a
Statistics button that will computer averages and deviations. Data that goes into such a
calculation can be selected by highlighting the relevant entries in the columns.
1 Particles in a box with two sections
Suppose that N particles are placed in a box with two sections (“left” and “right”). Suppose
that initially all particles are in the left section and at t = 0 a partition between the sections
is removed. Let n(t) be the number of particles in the left section at time t.
a) How do you expect n(t) will evolve as time passes?
This can be simulated using one of the text simulators. Run the “launcher” and select
Approach to equilibrium → Particles in a box. This will open a controller window where the
number of particles can be adjusted by setting N in the relevant box (and hitting Initialize).
The simulation describes the number of particles on a single side of the box.
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b) Starting with N = 20, run the simulation. Does n appear to approach a fixed value?
If so what is the fixed value? How large are the typical fluctuations in n? Does n ever
return to 20?
c) Starting with N = 200, run the simulation. Does n appear to approach a fixed value?
If so what is the fixed value? How large are the typical fluctuations in n? Does n ever
return to 200?
d) Starting with N = 2000, run the simulation. Does n appear to approach a fixed value?
If so what is the fixed value? How large are the typical fluctuations in n? Does n ever
return to 2000?
e) In which case, N = 20, N = 200 or N = 2000, is there are more distinct equilibrium
state. What is the equilibrium state?
f) The simulation lets you record the average number of particles n and the standard
deviation in the number of particles, σ, which quantifies the fluctuations in n. In each
case, after the simulation has appeared to reach equilibrium, determine n and σ for a
period during which the system is close to equilibrium.
A measure of the typical size of
fluctuations is σ/n. Determine this for each case. How does it behave as N increases?
What does this imply about the precision of the equilibrium state as N increases?
2 Interacting systems in equilibrium
Much of thermodynamics deals with systems that interact. The usual consideration here,
is that there are two isolated systems that are in equilibrium states. These are brought
into thermal contact and they than reach a new equilibrium state. The issue is to find the
common property that describes this new equilibrium state. The simulation Identification of
the Temperature explores this. Run the “launcher” and select Identification of the Temperature
and, using the default parameters, click “Initialize.”
The simulation shows two systems, which by default are thermally isolated. They can be
brought into thermal contact by clicking the “Contact” button.
a) Run the simulation with the two systems isolated. The simulation will display fluctuating energies for both systems. By averaging over a reasonable duration, record the
average kinetic and potential energies per particle for each system. Use these to determine the total energy for each subsystem. Are any of these quantities the same for each
system?
b) Without resetting, click the “Contact” button. Which of the energies change?
c) After the systems have reached a common equilibrium record the average kinetic and
potential energies per particle for each system. Use these to determine the total energy
for each subsystem. Which way did energy flow?
d) After the two systems have reached a common thermal equilibrium, which quantity is
the same for the two systems? Given that the temperature of two systems in thermal
equilibrium must be the same, which quantity best represents temperature?
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3 Constant volume gas thermometer
A constant volume gas thermometer consists of a gas inside a flask whose volume
is fixed. The pressure of the gas is monitored. The container can be immersed
inside any fluid and the pressure can be monitored. The flask is immersed
into fluid A and the pressure is monitored. After the pressure has settled it is
recorded, giving a pressure of 10 kPa. Then the flask is removed and immersed
in fluid B, which is isolated from fluid A. After the pressure has settled it is
recorded, giving a pressure of 20 kPa.
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a) List the variables that can be used to describe the state of the gas inside the flask. For
each variable, describe whether it is the same (after settling) for fluid A as for fluid B.
Is the state of the gas the same for fluid A as for fluid B? Explain your answer.
b) Would fluid A and fluid B be in thermal equilibrium if they were placed into contact with
each other? Do they have the same or different temperatures? Explain your answers.
4 Venus’ atmosphere
The atmosphere of Venus consists of 96.5% carbon dioxide and 3.5% molecular nitrogen (N2).
a) Determine the mass of one mole (6.02 × 1023 molecules) of Venus’ “air.”
b) The surface temperature of Venus is 740 K and the surface pressure 9.2 × 106 Pa. Determine the density of Venus’ atmosphere.
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