Ideal Gas Law

The law of Boyle and Marriotte relates the pressure $p$ of a gas and its volume $V$ at a constant temperature -

$pV = \text{constant}$

The Law of Gay-Lussac describes the change in the volume of a gas caused by the change in temperature -

$V=V_0 + \alpha T$ where $\alpha$ is the the thermal expansion factor for gases, $\dfrac{1}{273} K^{-1}$ .

Combining the above two equations we get the equation of state of an ideal gas -

$\frac{pV}{T} = R = \text{constant}$

The quantity $\text{R}$ is known as the universal gas constant. Hence,

$\text{R} = \dfrac{(1.013\times 10^5 \text{Pa})(22.41 \times 10^{-3} \text{m}^3)}{273 \text{K}} = 8.31 \text{J/mol}\cdot \text{K}$

The universal gas constant is thus in fact the energy acquired or lost by the molecules of one mole of a gas if its temperature is varied by one degree.

#Chemistry

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Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
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