Example 2.4 Predicting the Melting Point
of Spherical Nanoparticles
The atomic diameter of silver is 320 pm. Predict the melting point of a
sample of Ag nanoparticles of size 100 nm. The bulk phase melting
point of silver is 961.8°C.
Solution 320 pm = 0.320 nm. Using the appropriate equation for
N/n from Table 2.1 (see Example 2.3), we have
N
n
=
4d
D
=
4 Â 0:320
100
= 0:0128
Using Equation 2.7 gives us the melting temperature of the nanoparticle:
T
n
mpt = T
b
mpt 1 −
1
2
N
n
= 961:8 1 −
1
2
 0:0128
= 955:6°C
2.3 THE FIRST LAW OF THERMODYNAMICS
The flow of energy is a vital characteristic of any process. Intuitively, one
assumes that processes occur when the energy of the system will be
lowered. For example, a rolling ball with a given amount of kinetic energy
will eventually come to rest (zero kinetic energy) as it converts its kinetic
energy to other forms such as heat due to friction with the surface and
the heat is transferred to the surroundings. Even though the ball loses
kinetic energy, the total energy of the system (ball) and surroundings
(surface) remains constant. The first law is a statement of the conservation
of energy. We will focus on three kinds of energy transfer: mechanical work,
heat flow, and electrical work. In particular, we will see how exchanges
among these three forms allow us understand processes in nanomaterials.
2.3.1 Work
Mechanical work (w) is a result of unbalanced forces. To understand this,
let’s consider a system comprised of a gas compressed in a cylinder with
volume V i and pressure P i (Figure 2.1). The surrounding environment has an
external pressure P ext . The piston (of cross-sectional area A) pushing against
the gas is held in position by pins. When the pins are removed the gas
expands to its new volume V 2 . The system has reached mechanical equilibrium because the new final pressure (P f ) equals the external pressure (i.e.,
P f = P ext ). We say that work has been done by the system on the surroundings.
THE FIRST LAW OF THERMODYNAMICS
29
of Spherical Nanoparticles
The atomic diameter of silver is 320 pm. Predict the melting point of a
sample of Ag nanoparticles of size 100 nm. The bulk phase melting
point of silver is 961.8°C.
Solution 320 pm = 0.320 nm. Using the appropriate equation for
N/n from Table 2.1 (see Example 2.3), we have
N
n
=
4d
D
=
4 Â 0:320
100
= 0:0128
Using Equation 2.7 gives us the melting temperature of the nanoparticle:
T
n
mpt = T
b
mpt 1 −
1
2
N
n
= 961:8 1 −
1
2
 0:0128
= 955:6°C
2.3 THE FIRST LAW OF THERMODYNAMICS
The flow of energy is a vital characteristic of any process. Intuitively, one
assumes that processes occur when the energy of the system will be
lowered. For example, a rolling ball with a given amount of kinetic energy
will eventually come to rest (zero kinetic energy) as it converts its kinetic
energy to other forms such as heat due to friction with the surface and
the heat is transferred to the surroundings. Even though the ball loses
kinetic energy, the total energy of the system (ball) and surroundings
(surface) remains constant. The first law is a statement of the conservation
of energy. We will focus on three kinds of energy transfer: mechanical work,
heat flow, and electrical work. In particular, we will see how exchanges
among these three forms allow us understand processes in nanomaterials.
2.3.1 Work
Mechanical work (w) is a result of unbalanced forces. To understand this,
let’s consider a system comprised of a gas compressed in a cylinder with
volume V i and pressure P i (Figure 2.1). The surrounding environment has an
external pressure P ext . The piston (of cross-sectional area A) pushing against
the gas is held in position by pins. When the pins are removed the gas
expands to its new volume V 2 . The system has reached mechanical equilibrium because the new final pressure (P f ) equals the external pressure (i.e.,
P f = P ext ). We say that work has been done by the system on the surroundings.
THE FIRST LAW OF THERMODYNAMICS
29