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Tutorial Problems and Questions

This document contains answers to two tutorial problems about condensed systems and statistical mechanics. The first summary explains that the change in enthalpy due to a change in pressure is small for condensed systems and can usually be neglected. The second summary derives an expression for the number of configurations of atoms on a lattice using Stirling's approximation and properties of factorials.

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Arman Khan
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91 views1 page

Tutorial Problems and Questions

This document contains answers to two tutorial problems about condensed systems and statistical mechanics. The first summary explains that the change in enthalpy due to a change in pressure is small for condensed systems and can usually be neglected. The second summary derives an expression for the number of configurations of atoms on a lattice using Stirling's approximation and properties of factorials.

Uploaded by

Arman Khan
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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Tutorial problems and questions

1. Show that it condnesed systems .

Answer

The change in enthalpy due to a change in pressure from to is given by (See 1)


where α is the isobaric coefficient of thermal expansion and is

the molar volume.

Typically, most of materials are considered at 1 atmospheric pressure (which is a very small
quantity by itself). Further, since the coefficient of expansion for condensed systems (liquids and
solids) is very small, the total change in enthalpy due to pressure changes is very small. Hence, it
can be neglected.

As an example, consider iron, for which , K -1 . Even an increase of


pressure from 1 to 100 atmospheres at 298 K thus increases the enthalpy by about 70 J or so,
which can be achieved just by increasing temperature by about 3 K.

2. Derive

Answer

where is the number of available states.

In the case of pure materials, there is only one state and hence , On the other hand,
for and atoms of types and respectively places on a lattice of sites,

Thus,

We can use Stirling's approximation which is valid for large , and which states
.

Thus,

But, .

Hence,

where we have also multiplied and divided the qualtity in the square brackets by .

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