Latent Heat
Latent heat is the heat released or absorbed by a body or a thermodynamic system during a process that occurs without a change in temperature. A typical example is a change of state of matter, meaning a phase transition such as the melting of ice or the boiling of water. The term was introduced around 1762 by Joseph Black. It is derived from the Latin latere (to lie hidden).
Two of the more common forms of latent heat encountered are latent heat of fusion (melting or freezing) and latent heat of vaporization (boiling or
condensing). These names describe the direction of energy flow when changing from one phase to the next: from solid to liquid, and to gas.
In both cases the change is endothermic, meaning that the system absorbs energy on going from solid to liquid to gas. The change is exothermic (the process releases energy) for the opposite direction.
A specific latent heat (L) expresses the amount of energy in the form of heat (Q) required to completely effect a phase change of a unit of mass (m) of a substance:
L = Q
m
supercritical fluid
Water phase diagram
Enthalpy
Enthalpy is a measure of the total energy of a thermodynamic system. It includes the internal energy, which is the energy required to create a system, and the amount of energy required to make room for it by displacing its
environment and establishing its volume and pressure.
The enthalpy is the preferred expression of system energy changes in many chemical, biological, and physical measurements, because it simplifies certain descriptions of energy transfer. This is because a change in enthalpy takes account of energy transferred to the environment through the expansion of the system under study.
The U term can be interpreted as the energy required to create the system, and the pV term as the energy that would be required to "make room" for the system if the pressure of the environment remained constant.
During a constant-pressure process:
The first law:
The difference in enthalpy does not involve the compression-expansion work; it reflects the heat added and other form of work (e.g., electrical).
H ⌘ U + P V
H = U + P V
U = Q + ( P V ) + W
other(heat added) + (compression work on the system) +(other work)
H = Q + W
other(P = const.)
C
P=
✓ @H
@T
◆
P
A better definition of CP (=> enthalpy capacity)
The standard enthalpy of formation of a compound is the change of
enthalpy that accompanies the formation of 1 mole of the compound from its elements, with all substances in their standard states.
H
2+ 1
2 O
2! H
2O
H = 286 kJ/mol
heat produced by burning hydrogenHeat conduction, transport theory
Heat conduction is the transfer of heat energy by microscopic diffusion and collisions of particles or quasi-particles within a body due to a temperature gradient. The microscopically diffusing and colliding objects include
molecules, electrons, atoms, and phonons.
The laws of heat conduction determine the time rate of heat transfer .
Q / A T t x
Q = ˙ k
tA dT dx
heat flux
~q = k
trT ~
Fourier's heat conduction law:
x
Conductivity, ideal gas
The mean free path of a particle, such as a molecule, is the average
distance the particle travels between collisions with other moving particles.
The magnitude of the mean free path depends on the characteristics of the system the particle is in:
where n is the number of target particles per unit volume, and σ is the effective cross sectional area for collision
` = 1 n
` = V /N
The average time between collisions between air molecules is around 10
-10s
air
T
1, U
1T
2, U
2Q ⇡ 1
2 (U
1U
2) = 1
2 C
V(T
2T
1) = 1
2 C
V` dT dx
The net heat flow across the border is:
k
t/ p T
1.7 Rates of Processes 43 Equation 1.64 confirms Fourier’s law, that the rate of heat conduction is di-
rectly proportional to the difference in temperatures. Furthermore, comparison to equation 1.60 yields an explicit prediction for the thermal conductivity:
kt = 1 2
CV! A ∆t = 1
2 CV
A!
!2
∆t = 1 2
CV
V ! v, (1.65)
where v is the average speed of the molecules. The quantity CV/V is the heat capacity of the gas per unit volume, which can be evaluated as
CV
V = f2N k V = f
2 P
T , (1.66)
where f is the number of degrees of freedom per molecule. Recall, however, that ! for a gas is proportional to V/N. Therefore the thermal conductivity of a given gas should depend only on its temperature, through v ∝ √
T and possibly through f . Over limited ranges of temperature the number of degrees of freedom is fairly con- stant, so kt should be proportional to the square root of the absolute temperature.
Experiments on a wide variety of gases have confirmed this prediction (see Fig- ure 1.19).
For air at room temperature and atmospheric pressure, f = 5 so CV/V =
5
2(105 N/m2)/(300 K) ≈ 800 J/m3·K. Equation 1.65 therefore predicts a thermal conductivity of
kt ≈ 12(800 J/m3·K)(1.5 × 10−7 m)(500 m/s) = 0.031 W/m·K, (1.67) only a little higher than the measured value of 0.026. Not bad, considering all the crude approximations I’ve made in this section.
The preceding analysis of the thermal conductivities of gases is an example of what’s called kinetic theory, an approach to thermal physics based on actual molecular motions. Another example was the microscopic model of an ideal gas presented in Section 1.2. While kinetic theory is the most direct and concrete approach to thermal physics, it is also the most difficult. Fortunately, there are
Figure 1.19. Thermal con- ductivities of selected gases, plotted vs. the square root of the absolute temperature. The curves are approximately lin- ear, as predicted by equation 1.65. Data from Lide (1994).
Helium
Neon Air
Krypton 0.02
10 √
T (√ K) kt(W/m·K)
15 20 25
0.04 0.06 0.08 0.10
Viscosity
Viscosity is a measure of the resistance of a fluid which is being deformed by either shear stress or tensile stress. In everyday terms (and for fluids
only), viscosity is "thickness" or "internal friction". Thus, water is "thin", having a lower viscosity, while honey is "thick", having a higher viscosity. Put simply, the less viscous the fluid is, the greater its ease of movement (fluidity).
Laminar shear of fluid between two plates. Friction between the fluid and the moving
boundaries causes the fluid to shear. The drag force required for this action is a measure of the fluid's viscosity.
⌧ = |F
x|
A = ⌘ du
xshear stress viscosity dy Liquid helium can dribble through molecule-thin cracks, climb up and over the sides of a dish, and remain motionless when its container is spun.
http://www.youtube.com/watch?v=TBi908sct_U
Diffusion
Diffusion is one of several transport phenomena that occur in nature. A distinguishing feature of diffusion is that it results in mixing or mass transport without requiring bulk motion. Thus, diffusion should not be confused with convection or advection, which are other transport mechanisms that use bulk motion to move particles from one place to another. In Latin, "diffundere"
means "to spread out".
Fick's laws of diffusion describe diffusion. They were derived by Adolf Fick in 1855.
Fick's first law relates the diffusive flux to the concentration under the
assumption of steady state. It postulates that the flux goes from regions of high concentration to regions of low concentration, with a magnitude that is
proportional to the concentration gradient (spatial derivative). In one (spatial) dimension, the law is
Fick's second law predicts how diffusion causes the concentration to change with time:
