Biological Physics: Energy, Information, Life

6.5. Open systems[[Student version, January 17, 2003]] 191

expanded compressed

heat (at lower temperature)

mechanical work heat (at higher temperature)

Figure 6.6:(Diagram.) Operating cycle of a heat engine.

That’s amusing, but...biological motors are not cylinders of ideal gas. Nor are they driven by
temperature gradients. Your body doesn’t have a firebox at one end and a cooling tower at the
other, like the electric company’s generating plant. So Chapter 10 will turn away from heat engines
to motors run bychemicalenergy. Our effort has not been wasted, though. The valuable lesson we
learned in this subsection is based on the Second Law, and so is quite general:

Free energy transduction is least efficient when it proceeds by the uncontrolled

release of a big constraint. It’s most efficient when it proceeds by the incremen-

tal, controlled release of many small constraints.

(6.20)

Your Turn 6e

Why do you suppose your body is full ofmolecular-size motors, takingtinysteps? Why do

youthink the electric company only succeeds in capturing a third of the energy content in coal,

wasting the rest as heat?

6.5.4 The biosphere as a thermal engine

The abstract definition of temperature (Equation 6.9) gives us a way to clarify the “quality of
energy” concept alluded to in Chapter 1. Consider again an isolated system with two subsystems
(Figure 6.1). Suppose a large, nearly equilibrium system “A” transfers energy ∆Eto system “B,”
which need not be in equilibrium. Then “A” lowers its entropy by ∆SA=−∆E/TA.According to
the First Law, this transaction raises the energy of “B” by ∆E.The Second Law says that it must
also raise the entropy of “B” by at least|∆SA|,because ∆SA+∆SB≥0.
Togive “B” the greatest possible energy per unit of entropy increase, we need ∆E/∆SBto
belarge. We just argued that this quantity cannot exceed ∆E/|∆SA|. Since the last expression
equalsTA,our requirement implies thatTAmust be large: High quality energy comes from a
high-temperature body.
More precisely, it’s not the temperature but the fractional temperaturedifference straddled
byaheat engine that determines its maximum possible efficiency. We can see this point in the
context of the process analyzed in the Example on page 189 and the following text. Our strategy
for extracting work from this system assumed that the first reservoir was hotter than the second,
orT>T′.Let’s see why exactly this was necessary.