9.3 Definition of Temperature
327
for molecules built into structures is long, while times for metabolic processes are
short.
Systems made from a large number of individual entities which interact and
exchange energy will likely evolve into an equilibrium state. To be alive, an
organism cannot be in a settled equilibrium state. There are processes in us that
keep us away from such a state. However, we can still apply most of the formalism
of thermodynamics during the ordinary processes within our cells and between
cells. This ability is reflected by the fact that thermodynamic variables, such as
temperature and pressure can be meaningful in life subsystems, because their
fluctuations may be much smaller than the averages used to define them.
9.3 Definition of Temperature
Observation shows and theory suggests that if two macroscopic systems are placed
in ‘thermal contact’, 6 the net flow of energy between them will cease after some
‘relaxation’ time. We then say the two bodies are in thermal equilibrium.
The following definitions of temperature are all equivalent:
1. All bodies which, when put in thermal contact, show no transfer of macroscopic
energy, have a common temperature. We find that if A 1 and A 2 have the same
temperature, and body A 2 and A 3 have the same temperature, then A 1 and A 3
will have the same temperature. This idea is sometimes referred to as the ‘zeroth
law of thermodynamics’. Also, if body A is put into thermal contact with body B
and energy flows from A to B, then we say body A is hotter. We find that if body
A is hotter than B and B is hotter than C, then A is hotter than C. In this way,
temperature is both transitive and reflexive, and we can categorize all bodies in
equilibrium into sets according to their temperature.
2. Some thermometers take advantage of the fact that most materials change volume
with changes of temperature. A common thermometer uses a selected liquid
material, such as mercury, put into a long thin closed cylindrical tube, with a
vacuum in the distal part of the tube. Changes in temperature can be seen by
the expansion or contraction of the material within the tube. Difficulties with
such thermometers arise if the temperatures needed to be measured are beyond
the range for a single phase of the material, or the material, in some range of
temperature, reduces in volume with increased temperature. For example, water
increases in volume while dropping in temperature from 4 to 0 ◦ C.
3. A more universal thermometer, but less convenient, uses an ‘ideal’ gas. 7 A certain
amount of gas is sealed in a volume, whose pressure can be monitored. To
measure temperature, the gas is put into thermal contact with a material whose
6 Two bodies in thermal contact are allowed to exchange energy, but not by work of one on the
other.
7 Dilute helium approximates an ideal gas.
327
for molecules built into structures is long, while times for metabolic processes are
short.
Systems made from a large number of individual entities which interact and
exchange energy will likely evolve into an equilibrium state. To be alive, an
organism cannot be in a settled equilibrium state. There are processes in us that
keep us away from such a state. However, we can still apply most of the formalism
of thermodynamics during the ordinary processes within our cells and between
cells. This ability is reflected by the fact that thermodynamic variables, such as
temperature and pressure can be meaningful in life subsystems, because their
fluctuations may be much smaller than the averages used to define them.
9.3 Definition of Temperature
Observation shows and theory suggests that if two macroscopic systems are placed
in ‘thermal contact’, 6 the net flow of energy between them will cease after some
‘relaxation’ time. We then say the two bodies are in thermal equilibrium.
The following definitions of temperature are all equivalent:
1. All bodies which, when put in thermal contact, show no transfer of macroscopic
energy, have a common temperature. We find that if A 1 and A 2 have the same
temperature, and body A 2 and A 3 have the same temperature, then A 1 and A 3
will have the same temperature. This idea is sometimes referred to as the ‘zeroth
law of thermodynamics’. Also, if body A is put into thermal contact with body B
and energy flows from A to B, then we say body A is hotter. We find that if body
A is hotter than B and B is hotter than C, then A is hotter than C. In this way,
temperature is both transitive and reflexive, and we can categorize all bodies in
equilibrium into sets according to their temperature.
2. Some thermometers take advantage of the fact that most materials change volume
with changes of temperature. A common thermometer uses a selected liquid
material, such as mercury, put into a long thin closed cylindrical tube, with a
vacuum in the distal part of the tube. Changes in temperature can be seen by
the expansion or contraction of the material within the tube. Difficulties with
such thermometers arise if the temperatures needed to be measured are beyond
the range for a single phase of the material, or the material, in some range of
temperature, reduces in volume with increased temperature. For example, water
increases in volume while dropping in temperature from 4 to 0 ◦ C.
3. A more universal thermometer, but less convenient, uses an ‘ideal’ gas. 7 A certain
amount of gas is sealed in a volume, whose pressure can be monitored. To
measure temperature, the gas is put into thermal contact with a material whose
6 Two bodies in thermal contact are allowed to exchange energy, but not by work of one on the
other.
7 Dilute helium approximates an ideal gas.