Biological Physics: Energy, Information, Life

10. Problems[[Student version, January 17, 2003]] 405

Problems

10.1Complex processes
Figure 10.29 shows the rate of firefly flashing as a function of the ambient temperature. (Insects
do not maintain a fixed internal body temperature.) Propose a simple explanation for the behav-
ior shown. Extract a quantitative conclusion and comment on why your answer is numerically
reasonable.

10.2Rescuing Gilbert
Sullivan suggested one possible modification of the G-ratchet; here is another, which we will call
the “F-ratchet.”
Weimagine that the rod in Figure 10.10 extends far to the right, all the way into another
chamber full of gas at a temperatureT′. The rod ends with a plate in the middle of the second
chamber; gas molecules bounce against this plate, giving random kicks to the rod. We further
suppose thatT′is greater than the temperatureT of the part of the mechanism containing the

0.1

0.2

0.3

0.4

3.3 3.32 3.34 3.36 3.38 3.4 3.42

flashing rate,

-^1 s

1000/T, K-1

Figure 10.29: (Experimental data.) Semilog plot of the frequency of flashing of fireflies (arbitrary units), as a
function of inverse temperature. [Data from Laidler, 1972.]

T

T ́

Figure 10.30: (Schematic.) The “F-ratchet,” an imagined thermal machine. Two chambers are maintained
at temperaturesTandT′respectively; the right-hand chamber contains gas. Thermal motion in the right-hand
chamber drives the shaft; its motion is rectified by the device in the left-hand chamber, perhaps lifting a weight
attached to a pulley.