Download General Physical Chemistry I

General Physical Chemistry I
Lecture 6
Aleksey Kocherzhenko
February 24, 2015"
Thermodynamics"
the capacity
to do work"
Ø  The branch of science that studies transformations of energy, in particular,
the transformation of heat into work and vice versa"
We will learn to quantify
heat shortly"
Mechanical work performed by a force:"
Elementary work" dA
= F~ · d~l
Elementary
displacement"
Energy conservation:"
Force"
Energy can be neither created nor destroyed,
but only converted from one form into another or moved from place to place"
Ø  Energy is released or absorbed in most chemical reactions"
Ø  Thermodynamics identifies chemical reactions that may or may not occur
and the equilibrium of these chemical reactions"
A thermodynamic system is (any) part of the universe
that we are currently interested in studying"
The surroundings is a much larger part of the universe
that the system may interact with "
Ø  We assume that when a system interacts with its
surroundings, the state of the system changes, but the
state of the surroundings does not (e.g., constant T )"
The first law of thermodynamics"
Open, closed, and isolated systems"
Open system: can exchange both particles and
energy with its surroundings "
Closed system: contains a constant number
of particles, but can exchange energy with
its surroundings "
Isolated system: can exchange neither particles,
nor energy with its surroundings "
If:"
Processes in a closed system:" ⌫
p = const
à isobaric"
V = const à isochoric"
“iso” = “same”"
T = const à isothermal"
For
perfect
gas
only:"
= const
) pV = const
)
)
V
T
p
T
= const
= const
Heat and work"
Ø  Heat – energy transferred as a result of temperature difference"
@ high T, molecules move faster"
à part of their energy can be transferred to slower molecules in collisions"
~ ):"
Ø  Work (performed by force F
F~
↵
d~l
dA = F~ · d~l
Displacement of object on
which the work is performed"
Force performing the work"
~
Scalar product:" F
· d~l = F~ d~l cos ↵
pS
F~ ? d~l ) dA = 0
F~ k d~l ) dA = dAmax
Ø  Can a gas perform work?"
à Yes, by expansion "
m
Ø  Forces acting on piston – ?" à In equilibrium,"
pext S + mg = pint S
How can we make the gas expand and move the piston? "
S
mg
pext S
Cylinder with piston"
Expansion work"
pS
dl :" gas volume changes by" dV = Sdl
If dl is very small à tiny volume change" ) p ⇡ const
Piston moves by
S
m
mg
pext S
Work performed on piston by gas:" dA
= pS dl = pdV
|{z}
=F
By convention, work performed
on system is positive (system gains energy): "dA
= pdV
Work performed by system is negative (system uses energy):" dA
Perfect gas law:" pV
= ⌫RT
à changing
=
pdV
⌫ and/or T changes p and/or V
"
Change amount of gas:" Zn (s) + 2HCl (aq)
! ZnCl2 (aq) + H2 (g)
(or, just pump gas into the cylinder)"
External pressure and weight of piston are constant
"à if conditions of gas inside cylinder change, it may expand/compress
" until pext S + mg = pint S holds again"
Maximum expansion work"
pS
Imagine that there is no external pressure:"
S
weightless piston," m
pext = 0
=0
A single molecule could send the piston flying off to infinity!"
Ø  Gas could expand without performing work!"
pext S
Ø  Work is only performed if there is an opposing force
(in reality, there always is)"
Gas will, obviously, not expand if "pext
>p
à maximum expansion work for pext = p at all stages of the expansion
(maximum possible opposing force)
"
à equivalent to saying that the piston is at equilibrium at all stages of the
expansion (forces are balanced: pext S = pS )"
A system that remains in mechanical equilibrium with its surroundings
at all stages of the expansion performs maximum expansion work"
If pext = p, expansion/compression can be reversed
by an infinitesimal change in pressure: such a process is called reversible "
Work performed in isothermal expansion"
Expansion at constant temperature:" T
= const
Assume that the external pressure balances the pressure
of the gas inside the cylinder at all times:" pext = p
Elementary work:"
dA =
pdV
Total work performed"
in expansion from Vi to Vf :"
A=
pS
S
m=0
pext S
Z
Vf
pdV
Vi
⌫RT
Perfect gas law:" pV = ⌫RT ) p =
V
Z Vf
dV
Vf > 0
if "Vf > Vi
) A = ⌫RT
= ⌫RT ln
V
Vi (expansion)"
Vi
Isothermal process,
temperature is constant"
Expansion work is negative"
Path-dependence of work"
Isothermal expansion"
Another way of getting
from Vi to V
"f
First, cool the gas
at constant volume"
(no expansion à no work performed)"
Then, let it expand as you
heat it at constant pressure"
pf
We calculated:"
For this process:"
Vf
⌫RT ln
Vi
A=0
The work doesn’t just depend on the initial
and final states of the system, but also on
how the system gets from one to the other"
=
A=
Z
Vf
pf dV =
Vi
pf (Vf
Vi )
The internal energy"
Internal energy of a system = sum of all the kinetic and potential contributions
to the energy of all the atoms, ions, and molecules in the system"
Ø  The origin for energy can be selected arbitrarily, so we are only concerned
with energy differences, not energy values as such"
Ø  The change in the internal energy of a system: " dU
= dA + dq
Work performed on the system (positive)
Heat transferred"
or by the system (negative) "
to the system (positive) or from the
Ø  Isothermal expansion of a perfect gas:" system to the surroundings (negative)"
ü  No interactions between atoms à potential energy = 0"
à Internal energy = kinetic energy"
Kinetic definition of temperature"
2Ek
T =
3kB
There is one-to-one
correspondence
between T and Ek!"
à No change in temperature =
= no change in kinetic energy = no change in internal energy"
à In an isothermal process, "T
= const ) dU = 0 ) dq =
dA
The first law of thermodynamics"
The change in the internal energy of a system: "dU
= dA + dq
Work performed on the system (positive)
Heat transferred"
or by the system (negative) "
to the system (positive) or from the
The first law of thermodynamics"
system to the surroundings (negative)"
Verbal statement: The
"
change in the internal energy of the system is the sum
of the heat transferred to the system and the work performed on it"
An isolated system does not exchange
energy with its surroundings, neither as
heat, nor as work: dq
" = dA = 0
) dU = 0
The first law of thermodynamics is
the law of energy conservation:
energy can be converted from one
form to another, but it cannot be
created or destroyed"
à Perpetual motion machines that perform more work
than they use energy cannot be created"
Internal energy as a state function"
The internal energy only depends
on the initial and final state of the
system (not on how it transferred
from one to the other)"
Ø  Quantities like that are referred
to as state functions"
Ø  Work is not a state function:
as we have seen, it depends on
the path by which the system got
from the initial to the final state "
Enthalpy"
Many processes, particularly chemical reactions, occur at
constant pressure (in open vessels), not at constant volume"
à Transferred heat ≠ change in internal energy"
Ø  Heat transfer in such processes is conveniently
characterized in terms of the enthalpy, defined as:"
H = U + pV
Positive for endothermic reactions "
At constant pressure:" dH
= dU + pdV
Negative for exothermic reactions"
At constant pressure, the heat
transferred to the system is
equal to the change in enthalpy "
Ø  The enthalpy is defined in terms of state functions only ( U,
and thus it is itself a state function"
p, V
),
Ø  Like the internal energy, the enthalpy is an extensive quantity: it depends
on the amount of substance, and molar enthalpy can be defined"