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Ideal-Gas Numericals

You're welcome to download, read, share, and even reuse it under the CC by-sa license. If it helps you, please consider citing it where you use it – that makes a big difference. If you can afford it, buying the paid pdf or printed edition supports the project and keeps it sustainable. (Right now, about 1 in 400 readers do – thank you if you're one of them ) Enjoy the book – it was a joy to write and share by Olivier Cleynen ISBN: 9781446710067 First edition in English (June 2025), Olivier Cleynen / thermodynamicsbook com Translated from the third edition of the French original [51] Copyright 2015, 2018, 2021, 2025 Olivier Cleynen Engineering Thermodynamics is released under a Creative Commons license: c b a Attribution – Share-Alike 4 0.

Figures (4)

Isotherms of an ideal gas for different temperatures. The curved lines are rectangular hyperbolae of the form y = a/x. They represent the relationship between pressure (on the vertical axis) and volume (on the horizontal axis) for an ideal gas at different temperatures: lines that are farther away from the origin (that is, lines that are nearer to the top right-hand corner of the diagram) correspond to higher temperatures.
Relationships between Boyle's, Charles's, Gay-Lussac's, Avogadro's, combined and ideal gas laws, with the Boltzmann constant k = .mw-parser-output .sfrac{white-space:nowrap}.mw-parser-output .sfrac.tion,.mw-parser-output .sfrac .tion{display:inline-block;vertical-align:-0.5em;font-size:85%;text-align:center;margin-left:.1em;margin-right:.1em}.mw-parser-output .sfrac .num{display:block;border-bottom:1px solid}.mw-parser-output .sfrac .den{display:block;line-height:1.5em}.mw-parser-output .sr-only{border:0;clip:rect(0,0,0,0);clip-path:polygon(0px 0px,0px 0px,0px 0px);height:1px;margin:-1px;overflow:hidden;padding:0;position:absolute;width:1px}⁠R/NA⁠ = ⁠n R/N⁠ (in each law, properties circled are variable and properties not circled are held constant)
Molecular collisions within a closed container (a propane tank) are shown (right). The arrows represent the random motions and collisions of these molecules. The pressure and temperature of the gas are directly proportional: As temperature increases, the pressure of the propane gas increases by the same factor. A simple consequence of this proportionality is that on a hot summer day, the propane tank pressure will be elevated, and thus propane tanks must be rated to withstand such increases in pressure.
Relationship between the six gas laws

Key Points

  • The ideal gas law, also called the general gas equation, is the equation of state of a hypothetical ideal gas.
  • The pressure exerted by the spring on the walls of the box is constant at p= 105 Pa regardless of its volume.
  • The volume increases and the pressure decreases, since the gas is doing work while it receives heat.
  • The temperature of a body is a quantity that indicates its level of internal excitation.
  • In conclusion, if the Kelvin–Planck statement is correct, then the Clausius statement must also be correct.
  • The mole fraction yi is constant when the amount of each substance is constant, so we have Œ@ ln.yip=pı/=@pT;fnig D 1=p.

Terms

Tap a term for a plain-language explanation.

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