192 Chapter 6. Entropy, temperature, and free energy[[Student version, January 17, 2003]]
The engine did workWon its power stroke (the left-pointing arrow in Figure 6.6). It doesn’t
change at all in one complete cycle. But it released a quantity of thermal energyQinto the cooler
reservoir during the contraction step, increasing the entropy of the outside world by at leastQ/T′.
Some of this entropy increase is compensated in the next step, where we raise the temperature
back up toT:Inthis process an amount of thermal energy equal toQ+Wflows out of the hotter
reservoir, reducing the entropy of the outside world by (Q+W)/T.Thenetchange in world entropy
is then
∆Stot=Q(T^1 ′−T^1 )−WT. (6.21)
Since this quantity must be positive, we see that we can get useful work out (that is,W>0) only
ifT′<T.Inother words,The temperature difference is what drives the motor.
Aperfectheat engine would convertallthe input thermal energy to work, exhaustingnoheat.
Atfirst this may seem impossible: SettingQ=0in Equation 6.21 seems to give a decrease in the
world’s entropy! A closer look, however, shows us another option. If the second reservoir is close to
absolute zero temperature,T′≈0, then we can get near-perfect efficiency,Q≈0, without violating
the Second Law. More generally,abig temperature difference,T/T′,permits high efficiency.
Wecan now apply the intuition gleaned from heat engines to the biosphere. The Sun’s surface
consists of a lot of hydrogen atoms in near-equilibrium at about 5600K.It’s not perfect equilibrium
because the Sun is leaking energy into space, but the rate of leakage, inconceivably large as it is, is
still small compared to the total. Thus we may think of the Sun as a nearly closed thermal system,
connected to the rest of the Universe by a narrow channel, like system “A” in Figure 6.1 on page
179.
Asingle chloroplast in a cell can be regarded as occupying a tiny fraction of the Sun’s output
channel and joining it to a second system “B” (the rest of the plant in which it’s embedded),
which is at room temperature. The discussion above suggests that the chloroplast can be regarded
as a machine that can extract useful energy from the incident sunlight using the large difference
between 5600Kand 295K.Instead of doing mechanical work, however, the chloroplast creates the
high-energy molecule ATP (Chapter 2) from lower-energy precursor molecules. The details of how
the chloroplast captures energy involve quantum mechanics, and so are beyond the scope of this
book. But the basic thermodynamic argument does show us thepossibilityof its doing so.
6.6 Microscopic systems
Much of our analysis so far has been in the familiar context of macroscopic systems. Such systems
have the comforting property that their statistical character is hidden: statistical fluctuations are
small (see Figure 6.2), so their gross behavior appears to be deterministic. We invoked this idea
each time we said that a certain configuration was “overwhelmingly more probable” than any other,
for example in our discussion of the Zeroth Law (recall Figure 6.2 on page 181).
But as mentioned earlier, we also want to understand the behavior of single molecules. This
task is not as hopeless as it may seem: We are becoming familiar with situations, where individual
actors are behaving randomly and yet a clear pattern emerges statistically. We just need to replace
the idea of a definite state by the idea of a definiteprobability distributionof states.