extensive property will generally yield an intensive value. An important
example is the intensive quantity molar volume (
V ), given as volume
(extensive) divided by the number of moles (extensive) (Equation 2.1):
V =
V
n
(2.1)
Example 2.1 The Molar Volume of Gold Nanoparticles
The density of a 100-nm gold nanoparticle is 19.30 g/cm
3
. Determine its molar volume in liters per mole.
Solution The units of molar volume are L/mol. Therefore
V is
related to the inverse of density:
1
19:30 g=cm
3
= 0:052 cm
3 =g
The relative atom mass of Au is 197 g/mol:
∴ 0:052 cm
3 =g
 197:0 g=mol
ð
Þ= 10:24 cm
3 =mol
Since there are 1000 cm
3 in 1 L,
V ¼
10:24 cm
3
=mol
1000 cm
3
=L
¼ 0:010 L=mol
Before moving on, it is worth discussing the thermodynamic variable
internal energy (or the corresponding intensive variable molar internal
energy). Internal energy is the energy contained within the system and
results from the thermal motion of molecules; for an ideal gas, it depends
only on temperature. More complex molecules and nanostructures have
additional contributions from rotational and vibrational motion
depending on their number of degrees of freedom. An increase in the
temperature of a system results in a larger internal energy of the system.
As a simple example of a thermodynamic system, let’s consider a simple
piston such as that shown in Figure 2.1. The piston encloses a gas at some
initial pressure P i , which comprises the system. Let’s say the system
absorbs heat from the surroundings. The absorption of heat will increase
the temperature and therefore the internal energy of the gas by increasing
the thermal motion of the gas particles. The increase in temperature
results in an increase of the pressure within the cylinder. This process
leads to a new state having a final pressure P f . In Section 2.3 we will
examine the energy changes that occur due to this expansion process.
TERMINOLOGY IN THERMODYNAMICS
19
example is the intensive quantity molar volume (
V ), given as volume
(extensive) divided by the number of moles (extensive) (Equation 2.1):
V =
V
n
(2.1)
Example 2.1 The Molar Volume of Gold Nanoparticles
The density of a 100-nm gold nanoparticle is 19.30 g/cm
3
. Determine its molar volume in liters per mole.
Solution The units of molar volume are L/mol. Therefore
V is
related to the inverse of density:
1
19:30 g=cm
3
= 0:052 cm
3 =g
The relative atom mass of Au is 197 g/mol:
∴ 0:052 cm
3 =g
 197:0 g=mol
ð
Þ= 10:24 cm
3 =mol
Since there are 1000 cm
3 in 1 L,
V ¼
10:24 cm
3
=mol
1000 cm
3
=L
¼ 0:010 L=mol
Before moving on, it is worth discussing the thermodynamic variable
internal energy (or the corresponding intensive variable molar internal
energy). Internal energy is the energy contained within the system and
results from the thermal motion of molecules; for an ideal gas, it depends
only on temperature. More complex molecules and nanostructures have
additional contributions from rotational and vibrational motion
depending on their number of degrees of freedom. An increase in the
temperature of a system results in a larger internal energy of the system.
As a simple example of a thermodynamic system, let’s consider a simple
piston such as that shown in Figure 2.1. The piston encloses a gas at some
initial pressure P i , which comprises the system. Let’s say the system
absorbs heat from the surroundings. The absorption of heat will increase
the temperature and therefore the internal energy of the gas by increasing
the thermal motion of the gas particles. The increase in temperature
results in an increase of the pressure within the cylinder. This process
leads to a new state having a final pressure P f . In Section 2.3 we will
examine the energy changes that occur due to this expansion process.
TERMINOLOGY IN THERMODYNAMICS
19