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Expert-verified Found in: Page 195 ### An Introduction to Thermal Physics

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.

See the step by step solution

## Step 1: Given information

The total pressure of the system is fixed.

## Step 2: Explanation

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 ### Want to see more solutions like these? 