An Introduction to Thermodynamics phần 4 ppsx

1

1

2

1

1

1

dV

dV

dS dV

dV

dS dS = +

0 (13) 1

2

2

1

1 ≥ 















= − dV

T

P

T

P

dS

(14)

T

H

S

∆

∆ =

108 96. J/mol K

373 15. K

40,657 J/mol ∆ = = ⋅ S vap

It is assumed that T = T and thus the total entropy is unchanged by a transfer of thermal 5

1 2

energy between the two parts. The constant-energy restriction of equation 12 is satisfied because

any work done by one part on the other can be compensated by such a transfer of thermal energy.

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Again consider a system constrained to constant total volume, and to have a uniform temperature.

Then, as before, we can write the total change in entropy that might result from a change in

volume of either part in the form

(T, V)

and, because total volume is constant, dV = - dV . Substitution of equation 12 gives 1 2

5

This proves that two bodies in equilibrium must have not only the same temperature but also the

same pressure. It also proves that, when two bodies in contact, at the same temperature, have

different pressures, the body at the higher pressure will tend to expand and compress the body at

the lower pressure.

ISOTHERMAL ENTROPY CHANGES. Entropy changes at a single temperature follow directly from

equation 5. (Calculations involving a temperature difference or temperature change will be

treated later.)

A change of phase, under equilibrium conditions, will be at constant temperature and

constant pressure. The thermal energy transfer, Q = Q , will be ∆H. Therefore, rev

For example, the entropy change for the melting of ice was found to be 1.22 J/g·K or 22.0

J/mol·K. The entropy of vaporization of water at 100 C is o

More typical liquids, not involving such strong intermolecular forces, have ∆S values of about vap

92 J/mol·K at their normal boiling points. This is known as Trouton’s rule.

The work done in a reversible, isothermal expansion of an ideal gas was found to be

(equation 10, Chapter 1) Wrev = - nRT ln V2 1 /V . For an ideal gas at constant temperature ∆E = 0

and therefore Q = -W . The entropy change is thus rev rev