Download Lecture 1: Thermodynamics

Lecture 1: Thermodynamics
CHEM 452: Physical Chemistry for Biochemists
“The proper study of biology should really begin with the
theme of energy and its transformations.”
- Biochemistry by Albert L. Lehninger
What is a chemical (or physical) system
How to keep track of all the particles (system and
surroundings)
Ideal and real gasses
Thermodynamics and the Greek view of the natural
world
Working problems.
A very brief review of Chemistry 152; Chapters 9 and 10 of
Zumdahl; The 4 laws of Thermodynamics
• Basic Physical ideas of energy:
K .E. = 12 mv 2
U = EIMG = 32 PV
P.E.gr = mgh
E = cp = hν Photon
P.E.Coul
Ze 2
=−
r
c = λν
• Work and heat transfer; system/surroundings; State Fns.
PV = nRT
w = F ⋅ h = − Pext ∆V
∆U = q + w
∆H = ∆U + ∆ ( PV )
C=
qrev
∆T
∆U = CV ∆T
∆H = CP ∆T
CP = CV + nR
∆S =
qrev
T
∆S ≥ 0
• System changes, compute w,q, ∆U, ∆H, ∆S (Cycles)
• Chemical Reactions (Batteries) at Constant P and T
G = H − TS
∆G = ∆H − T ∆S
∆G = ∆Grxn ∆X
Q( X ) 
0
∆Grxn = ∆Grxn
+ RT ln Q ( X ) = RT ln 
K 

o
1 1
∆H rxn
K2
ln
=−
 − 
K1
R  T2 T1 
∆Grxn = −nFECell
0
∆Grxn
= RT ln K
Thermodynamics
•“set of tools” that describes the macroscopic properties of equilibrium
systems
•entirely empirical science
•based on four laws
0th law
1st law
2nd law
3rd law
defines
temperature
defines
energy
defines
entropy
provides a
numerical value
to entropy
Thermodynamics involves a lot of book-keeping, i.e. accounting for
energy/matter exchanges that help us predict the tendencies of
atoms and molecules to react, change their volume, their phase.
Carbon cycle
Thermodynamic cycles
Proton transport in ion channels
Nature 438, 975-980 (15 December 2005)
http://earthobservatory.nasa.gov/Library/CarbonCycle/Images/carbon_cycle_diagram.jpg
Otto engine
Energy is used to
generate heat; heat is
used (goes into the
engine) and generates
work; work comes out
of the engine. The
engine (the system) is
unchanged.
Definitions
System E.G.:
Gas in a box
Mass on a Spring
system
boundary
surroundings
Systems can be classified as:
Open: mass and energy can be transferred between system and
surroundings
Closed: energy can transfer but not mass
Isolated: Neither energy nor mass can be transferred between system
and surroundings
Definitions: What do we mean by energy in a system?
The energy is the sum of the kinetic and the potential energies.
We only look for changes in the energy.
Let’s Consider the energy in a mass on a spring (the Harmonic Oscillator)
Follow the energy as an isolated system
Follow the energy when the mass can interact with the
surroundings.
Apply the same analysis to the gas in a cylinder (or box).
How do we describe a system at equilibrium?
Thermodynamic variables or state variables
temperature T, pressure P and volume V, moles n
Variables are extensive or intensive
Extensive
•Sum of the properties of the system’s components.
•Depends on the size of the system
•Volume (V), Area (A), # of moles (n)
Intensive
•Independent of the size of the system
•Temperature (T), Pressure (P) and concentration
We can define equations of state such as the Ideal gas law
PV = nRT
n
C=
V
n
P = RT
V
P = C ⋅ RT
Identify the extensive and intensive variables.
m
d = = M ⋅C
V
Zeroth Law of Thermodynamics: definition of temperature
A
C
B
C
heat conducting wall
If A and C are at thermal equilibrium, i.e. at the same
temperature, and B and C are at thermal equilibrium, then it
follows that A and B are at thermal equilibrium, i.e. at the
same temperature.
Charles Law: Ideal gases can be thermometers
nR
P=
T
V
P = xT + g
g = −273.15°C
At low density All Gasses behave
as ideal gasses
Ideal gases
PV = nRT = N A kT
n
P = RT = ρ RT
V
k = Boltzmann constant
ρ= density
A = Avogadro’s number
R = gas constant
 ∂U 

 =0
 ∂V T
 ∂H 

 =0
 ∂P T
Internal energy
and Enthalpy for
an ideal gas
depend only on
temperature
Isotherm at 700 K
Van der Waals Equation of state
Units of the constants?
2
nRT
na
P=
− 2
V − nb V
a
b
2

n a
 P + 2  (V − nb ) = nRT
V 

Pressure correction
accounts for
interaction potential
between molecules
Volume correction
accounts for finite
size of the gas
molecules
volume2 mole-2 pressure
Pa m6 mol-2
volume mole-1
m3 mol-1
Dalton’s Law of Partial Pressures: Ideal Gas Mixtures
Ptotal = P1 + P2 + P3 + ... = ∑ Pi
i
RT
Pi = ni
V
ni
χi =
nTot
RT RT
PTot = ∑ Pi = ∑ ni
=
V
V
i
i
⇒
∑χ
i
=1
Partial pressure
of the ith gas in
the mixture
i
RT
∑i ni = V nTot
Example: A mixture of 1 mole of methane and 4 moles of
ethane are held at a pressure of 10 bar. What are the mole
fractions and partial pressures of the two gases?
Ptotal = Pmethane + Pethane = 10bar
Ptotal RT Pi
=
=
ntotal
V
ni
Pi =
ni
Ptotal = xi Ptotal
ntotal
ntotal = nmethane + nethane = 1mole + 4moles = 5moles
Pmethane
Pethane
nethane
4moles
10bar = 8bar
=
Ptotal =
5moles
ntotal
xmethane
xethane
nmethane
1mole
10bar = 2bar
=
Ptotal =
5moles
ntotal
nmethane
=
= 0.2
ntotal
nethane
=
= 0.8
ntotal
Key points of today’s lecture
Thermodynamics describes macroscopic properties of equilibrium
systems
There are 4 laws of thermodynamics
Definitions: system, surroundings, boundary, state variables,
extensive, intensive properties
Definition of temperature: 0th law of thermodynamics
Defining a temperature scale
Ideal gases
Real gases
Partial pressures of ideal gasses