# PistonCylinder:Problems:Level 2

Introduction |

Background |

Basic Layout |

Examples |

Problems |

Run Simulation |

Assessment |

Credits |

Etomica Modules |

*These problems are suitable for students in a thermodynamics course*

**Problem 1.**

Using an appropriate analysis of the data taken in Level 1 Problem 2, evaluate the second virial coefficient for this fluid at each temperature.

**Problem 2.**

Perform measurements for the ideal-gas model. Set the system at 1000 K and 1000 bar, start the simulation and let it run for a time until the density equilibrates. Then set the simulation to run adiabatically. Now slowly lower the pressure to 800 bar, then 600, 400, 200, and finally 100 bar. At each pressure, run the simulation for a short time to measure the temperature and density. Plot your data, and compare it to the formula for adiabatic expansion of an ideal gas.

Now reset the simulation and put the system at the same initial condition of 1000K and 1000 bar. Set the system to adiabatic operation, and then quickly slide the pressure down to 100 bar. Observe the resulting values taken by the density and temperature. Explain differences with the results seen when you performed the expansion slowly.

**Problem 3.**

Perform problem 2 except with the purely repulsive potential.

**Problem 4.**

Perform problem 2 except with the repulsive + attractive potential.

**Problem 5.**

Fit your data taken in Problem 1 of Level 1 to an equation of state, such as van der Waals or Redlich-Kwong, or another of your choice. Take additional data for the "Repulsion and attraction" model, using different choices for one or more of the model parameters (core diameter, epsilon, lambda, mass). Fit the equation of state to data for each choice of model parameters. Do you observe any correlation between the equation-of-state parameters determined by the fits, and the parameters of the model?