368
9 Bioenergetics
∂x
∂z
y
=
1
∂z/∂x| y
.
(9.121)
The relation Eq. (9.114) comes from applying Eq. (9.120).
9.17 Pressure in Multistate and Multicomponent Systems
Given that life systems on Earth rely on water for their biological activity, the nature
of evaporation and condensation of water from exposed surfaces is of considerable
importance. Also, because biological cells hold interior concentrations of some salts
and other compounds that differ from their exterior concentrations, osmotic pressure
across cell walls affects how the cell operates. Biological cells have developed
systems for both passive and active control of each of these pressures.
The air in your lungs is quickly saturated by water vapor and other gases from the
inner surface of alveoli. The surface of the tiny sacks used to transfer oxygen to your
blood, and carbon dioxide out, have a wet membrane lining next to the ventilating
gases of the air. A variety of volatiles dissolved in that wet membrane can move
across the liquid-gas boundary, changing the gas vapor pressure.
For another example, your skin evaporates water into the air, as does a lake. Just
above your skin, and just above the lake, the vapor pressure of water approaches a
saturation value.
When there are a multitude of species of materials in several phases, we can
ask how many independent intensive thermodynamic variables, f , are needed to
describe the thermodynamic equilibrium and near equilibrium states. Willard Gibbs
derived the result: f = c − p + 2, where c is the number of component species, p
the number of phases. The relation is called the ‘Gibbs’ phase rule’. For example,
applied to water (one component species) in three phases (solid, liquid, and gas),
f = 1 − 3 + 2 = 0, which means that if all three phases of water are in
equilibrium, there is a unique state (called the ‘critical point’ with fixed values of
the temperature and pressure: T c = 647 ◦ K, p c = 22.064 MPa). If there are two
phases, then f = 1, which allows equilibrium points on a line (phase boundary)
in a pressure vs temperature (p-T ) plot. When two phases exist near equilibrium,
any heat added to the system goes into energy needed to change the phase (e.g.
liquid water to vapor water), and not to changes of temperature. (Excursions into
thermodynamically unstable regions are possible to observe, such as in superheated
liquids and supercooled gases .) Water in a single phase (f = 2) can be near
equilibrium for points on a surface in a p-V -T plot, as depicted in Fig. 9.7.
9 Bioenergetics
∂x
∂z
y
=
1
∂z/∂x| y
.
(9.121)
The relation Eq. (9.114) comes from applying Eq. (9.120).
9.17 Pressure in Multistate and Multicomponent Systems
Given that life systems on Earth rely on water for their biological activity, the nature
of evaporation and condensation of water from exposed surfaces is of considerable
importance. Also, because biological cells hold interior concentrations of some salts
and other compounds that differ from their exterior concentrations, osmotic pressure
across cell walls affects how the cell operates. Biological cells have developed
systems for both passive and active control of each of these pressures.
The air in your lungs is quickly saturated by water vapor and other gases from the
inner surface of alveoli. The surface of the tiny sacks used to transfer oxygen to your
blood, and carbon dioxide out, have a wet membrane lining next to the ventilating
gases of the air. A variety of volatiles dissolved in that wet membrane can move
across the liquid-gas boundary, changing the gas vapor pressure.
For another example, your skin evaporates water into the air, as does a lake. Just
above your skin, and just above the lake, the vapor pressure of water approaches a
saturation value.
When there are a multitude of species of materials in several phases, we can
ask how many independent intensive thermodynamic variables, f , are needed to
describe the thermodynamic equilibrium and near equilibrium states. Willard Gibbs
derived the result: f = c − p + 2, where c is the number of component species, p
the number of phases. The relation is called the ‘Gibbs’ phase rule’. For example,
applied to water (one component species) in three phases (solid, liquid, and gas),
f = 1 − 3 + 2 = 0, which means that if all three phases of water are in
equilibrium, there is a unique state (called the ‘critical point’ with fixed values of
the temperature and pressure: T c = 647 ◦ K, p c = 22.064 MPa). If there are two
phases, then f = 1, which allows equilibrium points on a line (phase boundary)
in a pressure vs temperature (p-T ) plot. When two phases exist near equilibrium,
any heat added to the system goes into energy needed to change the phase (e.g.
liquid water to vapor water), and not to changes of temperature. (Excursions into
thermodynamically unstable regions are possible to observe, such as in superheated
liquids and supercooled gases .) Water in a single phase (f = 2) can be near
equilibrium for points on a surface in a p-V -T plot, as depicted in Fig. 9.7.