Page 51 - Modern physical chemistry

40 Gases and Collective Properties

Boyle's law, an approximate law summarizing experimental results, states that the
volume of a gas varies inversely with its pressure when the temperature is fixed:
PV = J(r).

Here r is the temperature on a suitable scale. On comparing this equation with (3.15),
we see that the translational energy E tr is a function of r alone in the ideal gas; thus

Example 3.2

How many newtons per square meter are there in 1 atmosphere?
The standard 1 atmosphere pressure supports a mercury column 760.00 rom high at
o °C, at a place where the acceleration due to gravity is 9.80665 m S·2 • The density of the
mercury is 13595.1 kg m-3.
Multiplying the mass per unit cross section of column by g, to convert the force, we have

2
P = (0.7600 mX13595.1 kg m-3 )(9.80665 m S-2) = 101325 N m- •
The newton per square meter is often called the pascal (Pa).
A most useful alternate standard is obtained on rounding off this value. The bar is
defined as the pressure 10 5 Pa Thus, it equals 750.06 torr.

Example 3.3
How many joules are there in 1 liter atmosphere?
In 1 liter, we have
3
v = (10 cm XlO-2 m cm- 1 t = 10- m .
3
3
3
Combining this with the result from example 3.2 gives us
PV = 101.325 J.
Similarly, in 1 liter bar, we have 100 J; in 1 cm 3 bar, 0.1 J.

3.3 Te~perature
Material systems consist of molecules, together with atoms, radicals, ions, free elec-
trons. These are continually being agitated and churned. In a gas, the particle units travel
more or less freely. In a liquid, the key ones oscillate about moving points; in a solid,
about fixed points.
At an interface between systems, the particle units on one side interact with those on
the other side. A molecule striking a wall with a high normal velocity and kinetic energy
tends to lose some of the corresponding energy to a sluggishly moving low energy wall
molecule. And a slowly moving attacking molecule tends to gain some kinetic energy from
a fast moving high energy wall molecule. In the long run, the kinetic energy tends to become
distributed over the different interacting degrees of freedom as randomly as possible.
The net energy transferred by such random processes across surfaces is called heat.
The random motion of the particle units is called thermal aqitation. When the energy of
thermal agitation in contacting bodies has become distributed as randomly as possible,