# PV-P diagram and the Boyle temperature

If we define *y = pv * and use the equation of the real gases, we obtain:

${y}^{3}-\left(bp+RT\right){y}^{2}+apy-ab{p}^{2}=0$

which will allow us to obtain the pv-p curves for a given temperature. The equation:

$b{y}^{2}-ay+2ap=0$

corresponds to the curve that connects the minimum values of the pv-p curve.

The files for this calculation are in folder `pvdiagrams/3_boyle/`

.

pmin [atm] | pvmin [atmL/mol] |
---|---|

-10.164 | 2.236 |

21.339 | 5.121 |

52.254 | 12.541 |

60.762 | 15.798 |

71.208 | 18.514 |

144.723 | 57.889 |

128.803 | 96.602 |

64.949 | 129.898 |

70.572 | 141.145 |

75.548 | 151.097 |

The calculated Boyle temperature is 1714.135 K.