# PistonCylinder:Problems:Level 1

Introduction |

Background |

Basic Layout |

Examples |

Problems |

Run Simulation |

Assessment |

Credits |

Etomica Modules |

*These problems are suitable for students in a material and energy balance course*

**Problem 1**

Measure the equation of state of this system for the ideal-gas model at each temperature available in the module. In particular, for each temperature evaluate the density N/V at pressures of 100, 200, 400, 600, 800, and 1000 bar. For each point, compute the compressibility factor Z = PV/NRT. Make plots of the data, both in the form of pressure versus density for each temperature (all three on the same plot), and (on another plot) the compressibility factor versus density. Do your data conform to ideal-gas behavior?

**Problem 2**

Perform the measurements and calculations described in Problem 1, but instead use the "Repulsion only" potential.

**Problem 3**

Perform the measurements and calculations described in Problem 1, but instead use the "Repulsion and attraction" potential.

**Problem 4**

Measure and plot the compressibility factor Z = PV/NRT for all three molecular model potentials, for pressures of 100, 500, and 1000 bar and temperatures 100, 600, and 1000K.

**Problem 5**

Begin the simulation with the system running adiabatically at the lowest pressure. Note the value of the density. Gradually increase the pressure using the slider, moving it as slowly as you can until you reach the highest pressure. Again record the density. Reverse the procedure, slowly decreasing the pressure to the lowest value. Is the low-pressure density the same as the value you started with?

Repeat this process, now increasing the pressure slowly, but then decreasing it as fast as you can. What is the final density?

Is the slow change or the fast change more reversible, in the sense that it brings you back to your initial condition?