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9 Bioenergetics
Heat conduction causes a change in the occupancy of the microscopic energy
levels as energy is being transported across a material, but, by definition, heat
energy transfer does not include coherent motion of material particles, which also
carries energy. In ordinary materials, the layers of material may interact though
local electric and magnetic fields, through incoherent collisions and by close-by
encounters as particles thermally move and vibrate. Through such proximity effects,
there will be a net tendency for energy to be transferred from the hotter layer to the
colder one, ‘the thermodynamic downhill direction’.
The flow of energy by heat conduction is a dissipative process, in that there is a
generation of more disorder in the colder material than a loss in the hotter one. 12
If a process is carried out with each change during the process only infinitesimally
far from an equilibrium state, then the sequence of states is called a ‘quasi-static
processes’. A quasi-static process may also have the property that if the system
is carried back to some initial state through the same quasi-equilibrium states, no
net entropy is produced in the overall process. In this case, the process is called
‘reversible’. Otherwise, the total disorder increases, and the process is irreversible.
A reversible process must be quasi-static, but a quasi-static process need not be
reversible.
Strong and dense materials have close-by molecules and relatively strong
molecular interactions, permitting quick and large energy transfers. Diamond is a
classic example of such a good conductor of heat. It is a very good conductor of
heat because the carbon atoms in diamond are in tight and close bonds. The heat
conductivity of metals is dominated by valence electrons which are free to quickly
carry thermal energy across the material, because the electrons are so much smaller
in mass compared to atoms. These electrons act like a gas in the metal.
Because of the pseudo-random nature of the heat-transfer process at the microscopic level and because of the large number of particles involved, the rate of heat
transfer δQ is proportional to the area A of material layers in contact, and inversely
proportional to the thickness dx of a given layer conducting heat. After all, with
all else the same, doubling the area of a layer will mean twice the heat will be
transferred. Similarly, doubling the thickness of a layer will result in twice the time
for the heat to transfer through both layers, at least for thin layers.
If the temperature throughout a layer of the material is constant, no heat will
transfer. One should expect, 13 and for most materials one finds, that for small
differences in temperature, the transfer rate is proportional to the difference in
temperature. Clearly, the rate of heat transfer will also depend on the material
‘carrying’ the heat.
12 A formal definition of disorder and its measure will be given in the chapter describing the
statistical basis of bio-energetics, Chap. 10.
13 A Taylor expansion of the heat-transfer rate through a layer of material as a function of
temperature difference across that layer will have a first term T , provided the first derivative
does not vanish. If the first term does not vanish, the next term, proportional to T 2 , can be made
negligible by taking the thickness of the layer, and therefore T , sufficiently small.
9 Bioenergetics
Heat conduction causes a change in the occupancy of the microscopic energy
levels as energy is being transported across a material, but, by definition, heat
energy transfer does not include coherent motion of material particles, which also
carries energy. In ordinary materials, the layers of material may interact though
local electric and magnetic fields, through incoherent collisions and by close-by
encounters as particles thermally move and vibrate. Through such proximity effects,
there will be a net tendency for energy to be transferred from the hotter layer to the
colder one, ‘the thermodynamic downhill direction’.
The flow of energy by heat conduction is a dissipative process, in that there is a
generation of more disorder in the colder material than a loss in the hotter one. 12
If a process is carried out with each change during the process only infinitesimally
far from an equilibrium state, then the sequence of states is called a ‘quasi-static
processes’. A quasi-static process may also have the property that if the system
is carried back to some initial state through the same quasi-equilibrium states, no
net entropy is produced in the overall process. In this case, the process is called
‘reversible’. Otherwise, the total disorder increases, and the process is irreversible.
A reversible process must be quasi-static, but a quasi-static process need not be
reversible.
Strong and dense materials have close-by molecules and relatively strong
molecular interactions, permitting quick and large energy transfers. Diamond is a
classic example of such a good conductor of heat. It is a very good conductor of
heat because the carbon atoms in diamond are in tight and close bonds. The heat
conductivity of metals is dominated by valence electrons which are free to quickly
carry thermal energy across the material, because the electrons are so much smaller
in mass compared to atoms. These electrons act like a gas in the metal.
Because of the pseudo-random nature of the heat-transfer process at the microscopic level and because of the large number of particles involved, the rate of heat
transfer δQ is proportional to the area A of material layers in contact, and inversely
proportional to the thickness dx of a given layer conducting heat. After all, with
all else the same, doubling the area of a layer will mean twice the heat will be
transferred. Similarly, doubling the thickness of a layer will result in twice the time
for the heat to transfer through both layers, at least for thin layers.
If the temperature throughout a layer of the material is constant, no heat will
transfer. One should expect, 13 and for most materials one finds, that for small
differences in temperature, the transfer rate is proportional to the difference in
temperature. Clearly, the rate of heat transfer will also depend on the material
‘carrying’ the heat.
12 A formal definition of disorder and its measure will be given in the chapter describing the
statistical basis of bio-energetics, Chap. 10.
13 A Taylor expansion of the heat-transfer rate through a layer of material as a function of
temperature difference across that layer will have a first term T , provided the first derivative
does not vanish. If the first term does not vanish, the next term, proportional to T 2 , can be made
negligible by taking the thickness of the layer, and therefore T , sufficiently small.