Chapter 1 Lecture

Biological PhysicsNelson

Updated 1st Edition

Slide 1-1

What the ancients knew

Slide 1-2

Announcements

• Study methods

– Read each chapter BEFORE class

– Do the homework exercises (hand in)

• Grading: Participation 30%

– Midterm report/presentation 35%

– Final report/presentation 35%

• One more irregular class on April 30 or May 6 …

• Those of you taking Advanced Physics 1 (AP1)

will be encouraged to take AP2, sorry.

Slide 1-3

Intro: Entropy and 2nd Law

• The second law of thermodynamics can be stated in terms of

entropy: No process is possible in which the total entropy of an

isolated system decreases.

• In Figure below, the entropy (disorder) of the ink-water system

increases as the ink mixes with the water. Spontaneous unmixing

of the ink and water is never observed.

Slide 1-4

However.

• Have you heard of the Belousov–Zhabotinskii

reaction?

• Watch this SHOW STOPPER:

http://www.youtube.com/watch?v=E-ZIXGgt8sI

• What is happening here? This is related to how

life can somehow defy the 2nd Law of

Thermodynamics

Slide 1-5

The Energy Analogy

• Energy is an abstract concept a bit like money

• Money is a nice analogy:

– KE = Cash; PE = Savings

– Work > 0 is earning money

– Work < 0 is paying bills

• Power is how much and over how long

– Earning a $1,000,000 over 100 years is worse

than earning 1000000/2400 = $416/month

• Conservation of energy more fundamental than

Newton’s laws and applies to things like

quantum mechanics

Slide 1-6

Conservative and Nonconservative Forces

• Examples of conservative forces include

• Gravity

• The static electric force

• The force of an ideal spring

• Nonconservative forces include

• Friction/Heat

• The electric force in the presence of changing

magnetism

Slide 1-7

Conservative and Nonconservative Forces

• A conservative force stores any work done against it, and

can “give back” the stored work as kinetic energy.

• For a conservative force, the work done in moving between

two points is independent of the path:

• A nonconservative force does not store work done

against it, the work done may depend on path, and the work

done going around a closed path need not be zero.

Slide 1-8

The cycle of life?

Slide 1-9

Conservation of Mechanical Energy

• By the work-energy theorem, the change in an object’s

kinetic energy equals the net work done on the object:

∆K = Wnet= Wext

• When only conservative forces act, the net work is the

negative of the potential-energy change: Wnet = –∆U

• Therefore when only conservative forces act, any change in

potential energy is compensated by an opposite change in

kinetic energy:

∆K + ∆U = 0

• Equivalently,

K + U = constant = K0 + U0

• Both these equations are statements of the law of

conservation of mechanical energy.

Slide 1-10

Conservation of energy with heat?

• Non-conservative forces do not store potential

energy, but they do change the internal energy of a

system.

• The law of the conservation of energy means that

energy is never created or destroyed; it only

changes form.

• This law can be expressed by including a change

in internal energy Uint = Etherm this is also a

change in thermal energy hence

K + U + Etherm = Wext

Slide 1-11

First law of thermodynamics

• Now consider a pan of water over a flame,

clearly Etherm > 0 but no external work is being

done.

• So we must include something else:

K + U + Etherm = Wext + Q

• Generally these systems are stationary:

K=U = 0 and this implies:

Etherm = Wext + Q

• This is the first law of thermodynamics for work

done on the system. If work done by => –Wext

Etherm= Q - Wext

Slide 1-12

Thermodynamics systems

• A thermodynamic system is any

collection of objects that may

exchange energy with its

surroundings.

• In a thermodynamic process,

changes occur in the state of the

system.

• Careful of signs! Q is positive

when heat flows into a system. W

is the work done by the system,

so it is positive for expansion.

(See the figure on the right.)

Slide 1-13

First law of thermodynamics

• First law of thermodynamics: The change in the internal energy U of a system is equal to the heat added minus the work done by the system: U = Q – W. (See figure on right.)

• The first law of thermodynamics is just a generalization of the conservation of energy.

• Both Q and W depend on the path chosen between states, but U is independent of the path.

• If the changes are infinitesimal, we write the first law as dU = dQ – dW.

Slide 1-14

Note: Work done during volume changes*

• Figures below show how gas molecules do work when the gas volume changes.

Slide 1-16

High to low quality energy

Slide 1-17

Free energy transducer

Slide 1-18

Approaches to understanding

Slide 1-19

Dimensional analysis can guess laws

• Consider the “viscous friction coefficient” ζ = F/v

with dimensions M/T and the “diffusion constant”

D with dimensions L2/T.

• Both ζ and D depend in very complicated ways

on the temperature, the shape and size of the

object, and the nature of the fluid.

• However now assume the product ζD actually

turns out to be simple.

• What is the relation?

Slide 1-20

Dimensional analysis can guess laws

• Consider the “viscous friction coefficient” ζ = F/v

with dimensions M/T and the “diffusion constant”

D with dimensions L2/T.

• Both ζ and D depend in very complicated ways

on the temperature, the shape and size of the

object, and the nature of the fluid.

• However now assume the product ζD actually

turns out to be simple.

• Using dimensional analysis the relation depends

on energy: ζD=Etherm

• Einstein used this to prove atoms are real!

Slide 1-21

Parity

Slide 1-22

The BIG picture

This chapter’s Focus Question.

Section 1.2 discussed the idea that the flow of energy, together with its

degradation from mechanical to thermal energy, could create order. We

saw this principle at work in a humble process (reverse osmosis,

Section 1.2.2 on page 12), then claimed that life, too, exploits this

loophole in the Second Law of thermodynamics to create—or rather,

capture—order. Our job in the following chapters will be to work out the

details of how this works. For example, Chapter 5 will describe how tiny

organisms, even single bacteria, carry out purposeful motion in search

of food, enhancing their survival, despite the randomizing effect of their

surroundings. We will need to expand and formalize our ideas in

Chapters 6 and 8. Then we’ll be ready to understand the self-assembly

of complicated structures in Chapter 8. Finally, Chapters 11–12 will see

how one paragon of orderly behavior, namely how nerve impulses

emerge from the disorderly world of single-molecule dynamics.

Slide 1-23

Useful equations

Slide 1-24

Homework

• Read over Chapter 2 (on the cell) and watch the

student videos.

• Do Problem 1.4 (Earth’s temperature) & 1.5

(Franklin’s experiment)

• Next week we start Chapter 3, so also start

reading that (some probability is involved as

well)