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FURTHER THOUGHTS ON ENERGY 35

‘Standard temperature’ has the value of 298 K exactly, which A‘thermostat’is a
◦
equates to just below 25 C. If both the pressure and the temper- device for maintain-
ature are maintained at these standard conditions, then we say the ing a temperature.
measurement was performed at ‘standard temperature and pres- Thermo is Greek for
sure’, which is universally abbreviated to ‘s.t.p.’ If the scientists ‘energy’ or ‘tempera-
at the equator and the Arctic Circle perform their work in thermo- ture’, and ‘stat’ derives
statically controlled rooms, both at s.t.p., then the results of their from the Greek root
statikos, meaning ‘to
experiments will be identical.
stand’, i.e. not move or
alter.

Why do we get warmed-through in front of a fire,
rather than just our skins?

The Maxwell–Boltzmann distribution of energies

If no heat was distributed, then our faces and those parts closest to the fire
would quickly become unbearably hot, while the remainder of our flesh would
continue to feel cold. Heat conducts through the body principally by the fire
warming the blood on the surface of the skin, which is then
pumped to other parts of the body through the circulatory
We often see this rela-
system. The energy in the warmed blood is distributed within
tionship called merely
cooler, internal tissues.
the ‘Boltzmann dis-
It is important to note how the heat energy is distributed around
tribution’, after the
the body, i.e. shared and equalized. Nature does not like diversity Austrian Physicist Lud-
in terms of energetic content, and provides many mechanisms by wig Boltzmann (1844–
which the energy can be ‘shared’. We shall discuss this aspect of 1906), who played a
thermochemistry in depth within Chapter 4. pivotal role in marrying
We can be certain that molecules do not each have the same thermodynamics with
energy, but a distribution of energies. The graph in Figure 1.9 statistical and molecu-
concerns the energies in a body. The x-axis gives the range of lar physics.
energies possible, and the y-axis represents the number of particles
in the body (molecules, atoms, etc.) having that energy. The graph
clearly shows how few particles possess a large energy and how
a few particles have a tiny energy, but the majority have lesser The thermodynamic
energies. We call this spread of energies the ‘Maxwell–Boltzmann temperature is the sole
variable required to
distribution’.
define the Maxwell–
All speeds are found at all temperatures, but more molecules
Boltzmann distribution:
travel at faster speeds at the higher temperatures.
raising the temperature
The distribution law depicted in Figure 1.9 may be modelled
increases the spread of
mathematically, to describe the proportions of molecules of molar energies.
mass M with energies E in the range E to E + dE that exist in