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Q 5.63

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An Introduction to Thermal Physics
Found in: Page 195
An Introduction to Thermal Physics

An Introduction to Thermal Physics

Book edition 1st
Author(s) Daniel V. Schroeder
Pages 356 pages
ISBN 9780201380279

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Short Answer

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.

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Step by Step Solution

TABLE OF CONTENTS :
TABLE OF CONTENTS

Step 1: Given information

The total pressure of the system is fixed.

Step 2: Explanation

The Gibbs free energy is given by:

G=U+P V-T S

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:

∂G∂P=V>0

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

role="math" localid="1647026301082" Vliq>Vgas∂G∂Pgas>∂G∂Pliq

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

Most popular questions for Physics Textbooks

Plot the Van der Waals isotherm for T/Tc = 0.95, working in terms of reduced variables. Perform the Maxwell construction (either graphically or numerically) to obtain the vapor pressure. Then plot the Gibbs free energy (in units of NkTc) as a function of pressure for this same temperature and check that this graph predicts the same value for the vapor pressure.

Derive the van't Hoff equation,

dlnKdT=ΔH°RT2

which gives the dependence of the equilibrium constant on temperature." Here ∆H° is the enthalpy change of the reaction, for pure substances in their standard states (1 bar pressure for gases). Notice that if ∆H° is positive (loosely speaking, if the reaction requires the absorption of heat), then higher temperature makes the reaction tend more to the right, as you might expect. Often you can neglect the temperature dependence of∆H°; solve the equation in this case to obtain

lnKT2-lnKT1=ΔH°R1T1-1T2

An inventor proposes to make a heat engine using water/ice as the working substance, taking advantage of the fact that water expands as it freezes. A weight to be lifted is placed on top of a piston over a cylinder of water at 1°C. The system is then placed in thermal contact with a low-temperature reservoir at -1°C until the water freezes into ice, lifting the weight. The weight is then removed and the ice is melted by putting it in contact with a high-temperature reservoir at 1°C. The inventor is pleased with this device because it can seemingly perform an unlimited amount of work while absorbing only a finite amount of heat. Explain the flaw in the inventor's reasoning, and use the Clausius-Clapeyron relation to prove that the maximum efficiency of this engine is still given by the Carnot formula, 1 -Te/Th

Repeat the previous problem for the opposite case where the liquid has a substantial negative mixing energy, so that its free energy curve dips |below the gas's free energy curve at a temperature higher than TB. Construct the phase diagram and show that this system also has an azeotrope.

When carbon dioxide "dissolves" in water, essentially all of it reacts to form carbonic acid, H2CO3:

CO2( g)+H2O(l)⟷H2CO3(aq)

The carbonic acid can then dissociate into H* and bicarbonate ions,

H2CO3(aq)⟷H+(aq)+HCO3-(aq)

(The table at the back of this book gives thermodynamic data for both of these reactions.) Consider a body of otherwise pure water (or perhaps a raindrop) that is in equilibrium with the atmosphere near sea level, where the partial pressure of carbon dioxide is 3.4 x 10-4 bar (or 340 parts per million). Calculate the molality of carbonic acid and of bicarbonate ions in the water, and determine the pH of the solution. Note that even "natural" precipitation is somewhat acidic.
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