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An Introduction to Thermal Physics
Found in: Page 163
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

Imagine that you drop a brick on the ground and it lands with a thud. Apparently the energy of this system tends to spontaneously decrease. Explain why.

The energy is transferred from the brick to the ground, so the energy of the system tends to spontaneously decrease.

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Step by Step Solution

TABLE OF CONTENTS :
TABLE OF CONTENTS

Given

A brick is dropped to the ground and it lands with a thud.

Energy of this system tends to spontaneously decrease, explain why?

Explanation

Helmholtz free energy can be determined by
F=U-T SWhere, F= Helmholtz free energy, U=Internal energy,T=absolute temperature of the system and S=entropy of the system.The total energy of the brick = kinetic energy + potential energy

From the law of energy conservation this is always constant.

When the brick hits the ground, its kinetic energy is zero, but the potential energy remains the same. The kinetic energy is redistributed into the thermal energy of the molecules of the brick and to the ground where the brick hits.

So a part of the energy is transferred from the brick to the ground.

Therefore the energy of the system tends to spontaneously decrease.

Most popular questions for Physics Textbooks

Consider again the aluminosilicate system treated in Problem 5.29. Calculate the slopes of all three phase boundaries for this system: kyanite andalusite, kyanite-sillimanite, and andalusite-sillimanite. Sketch the phase diagram, and calculate the temperature and pressure of the triple point.

What happens when you spread salt crystals over an icy sidewalk? Why is this procedure rarely used in very cold climates?

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.

In this problem you will derive approximate formulas for the shapes of the phase boundary curves in diagrams such as Figures 5.31 and 5.32, assuming that both phases behave as ideal mixtures. For definiteness, suppose that the phases are liquid and gas.

(a) Show that in an ideal mixture of A and B, the chemical potential of species A can be written μA=μA°+kTln(1-x)where A is the chemical potential of pure A (at the same temperature and pressure) and x=NB/NA+NB. Derive a similar formula for the chemical potential of species B. Note that both formulas can be written for either the liquid phase or the gas phase.

(b) At any given temperature T, let x1 and xg be the compositions of the liquid and gas phases that are in equilibrium with each other. By setting the appropriate chemical potentials equal to each other, show that x1 and xg obey the equations =1-xl1-xg=eΔGA°/RT and xlxg=eΔGB°/RT and where ΔG° represents the change in G for the pure substance undergoing the phase change at temperature T.

(c) Over a limited range of temperatures, we can often assume that the main temperature dependence of ΔG°=ΔH°-TΔS° comes from the explicit T; both ΔH° and ΔS° are approximately constant. With this simplification, rewrite the results of part (b) entirely in terms of ΔHA°,ΔHB° TA, and TB (eliminating ΔG and ΔS). Solve for x1 and xg as functions of T.

(d) Plot your results for the nitrogen-oxygen system. The latent heats of the pure substances areΔHN2°=5570 J/mol and ΔHO2°=6820 J/mol. Compare to the experimental diagram, Figure 5.31.

(e) Show that you can account for the shape of Figure 5.32 with suitably chosen ΔH° values. What are those values?

Compare expression 5.68 for the Gibbs free energy of a dilute solution to expression 5.61 for the Gibbs free energy of an ideal mixture. Under what circumstances should these two expressions agree? Show that they do agree under these circumstances, and identify the function f(T, P) in this case.
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