A single relation ties pressure, volume and temperature for a fixed amount of ideal gas. Knowing the two equivalent forms, and that temperature is always in kelvin, handles almost every gas calculation.
An ideal gas obeys pV = nRT = NkT, with T in kelvin. The Boltzmann constant links the two forms: k = R / N₊.
For a fixed amount of ideal gas the three quantities are tied by one relation. Squeeze the volume and the pressure rises; warm the gas and the pressure rises. The simulation lets you hold one quantity fixed and see how the other two trade off through pV = nRT.
The equation of state can be written per mole as pV = nRT, with the molar gas constant R, or per molecule as pV = NkT, with the Boltzmann constant k. The two constants are linked by k = R / N₊. In both forms the temperature must be the thermodynamic temperature in kelvin, and for a fixed mass pV / T stays constant.
Four quick checks on the gas laws, the two forms of the equation of state, and the Boltzmann constant. Each correct answer earns XP and lights this skill on your star map.
For a fixed mass of ideal gas at constant volume, the pressure is proportional to:
The equation pV = NkT is written in terms of:
The Boltzmann constant k is related to the molar gas constant R and the Avogadro constant N₊ by:
0.50 mol of an ideal gas at 300 K occupies 0.020 m³. Its pressure pV = nRT is about:
Temperature in pV = nRT must always be in kelvin. Keep the two forms apart: pV = nRT uses moles n and R, while pV = NkT uses the number of molecules N and k = R / N₊; never mix n with k or N with R. The shortcut pV ∝ T applies only to a fixed mass of gas.
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