Direct Energy, 2018a

178 8.4 Ideal Gas Law
8.4 Ideal Gas Law
In most materials, if we know three of the four thermodynamic properties,
volume, pressure, temperature, and entropy, we can derive the fourth property
as well as other thermodynamic measures. Such materials are called
simple compressible systems [109, 102]. For such materials, the ideal gas
law relates pressure, volume, and temperature.
PV = NRT. (8.14)
While this is not a mathematical law, it is a good description of gases, and
it can be used as a rough approximation for liquids and solids. Consider
a container lled with a gas. If the volume of the container is compressed
while the temperature is kept constant, the pressure increases. If the gas is
heated and the pressure is kept constant, the volume increases. The energy
stored in a gas that undergoes change in volume at constant temperature
is given by
ˆ
E = PdV (8.15)
where the change in energy is specied by
ΔE = PΔV. (8.16)
The ideal gas law can be written incorporating entropy as
PV = ST. (8.17)
For example, consider a 10 L tank that holds 5 mol of argon atoms. The
argon gas is at a temperature of T =15 ◦ C. Find the pressure in the tank
in pascals and in atm. We begin by converting the volume and temperature
to more convenient units, V =0.01 m 3 and T = 288.15 K. Next, the ideal
gas law provides the pressure in Pa.
P = NRT
V = 5 mol · 8.314 J
mol·K · 288.15 K
=1.20 · 10 6 Pa (8.18)
0.01 m 3
Finally, we convert the pressure to the desired units.
P =1.20 · 10 6 Pa ·
1 atm
101325 Pa
=11.8 atm (8.19)
As another example, consider a container that holds neon atoms at a
temperature of T =25 ◦ C. Assume that the pressure in the container is 10