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Q 5.63

Expert-verifiedFound in: Page 195

Book edition
1st

Author(s)
Daniel V. Schroeder

Pages
356 pages

ISBN
9780201380279

Everything in this section assumes that the total pressure of the system is fixed. How would you expect the nitrogen-oxygen phase diagram to change if you increase or decrease the pressure? Justify your answer.

The phase area will get smaller.

The total pressure of the system is fixed.

The Gibbs free energy is given by:

$G=U+PV-TS$

At constant volume and entropy, the change in Gibbs free energy is as follows:

$dG=dU+VdP-SdT$

As a result, as the pressure rises, the Gibbs free energy rises, resulting in:

$\frac{\partial G}{\partial P}=V>0$

Because the volume of the liquid is less than that of the gas,:

role="math" localid="1647026301082" ${V}_{liq}>{V}_{gas}\phantom{\rule{0ex}{0ex}}{\left(\frac{\partial G}{\partial P}\right)}_{gas}>{\left(\frac{\partial G}{\partial P}\right)}_{liq}$

As a result, if the slope of the curve increases or decreases, it will not increase or decrease in the same trend, implying that the phase area will shrink and phase area will get smaller

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