Second law of thermodynamics
A small amount of heat Q flows out of a
A small
amount
of heat
flows
outsystem
of a hot system A
hot system
A (350K)
into
a cold
(350K)
into aWhich
cold of
system
B (250K). Which of the
B (250K).
the following
correctly
following
correctly
describesdescribes
the entropythe entropy changes that
changes
result?are
(Thethermally
systems are
result?
(Thethat
systems
isolated from the
isolated from the rest of the
restthermally
of the universe.)
universe.)
|∆SA | > |∆SB|
2. |∆SB | > |∆SA|
3. |∆SA| = |∆SB|
4. It cannot be
determined from
the information
given
1.
Studio PHY-2054C Spring 2017
1
Recitation 1/24/2017
Second law of thermodynamics
Suppose
a small of
amount
heat Q
flows
from
A small
amount
heatofflows
out
of a
cold system B
a system A at low temperature (250K) to a system
(250K) into a hot system A (350K). Which of the
B
following
must be true
regarding
thefollowing
entropy of the
at high temperature
(350K).
Which of the
rest
of be
thetrue
universe
during
this of
process?
must
regarding
the entropy
the rest of
the universe during this process?
1.
2.
3.
4.
5.
It increases by an amount
greater than (|∆SA| - |∆SB|)
It increases by an amount
less than (|∆SA| - |∆SB|)
It decreases
It stays the same
It cannot be determined
from the information given
Studio PHY-2054C Spring 2017
2
Recitation 1/24/2017
removed and the system reaches equilibrium again, how
does the new internal energy of the gas compare to the
internal energy of the original system?
Second law of
1. thermodynamics
The energy increases
The energy decreases
The
stays
Suppose an isolated3.box
of energy
volume
2V the
is
same
divided into two equal compartments.
An ideal
4. There is not enough
gas occupies half of theinformation
containertoand
the
determine
other half is empty.
the answer
2.
•
When the partition separating the two halves
of the box is removed and the system
reaches equilibrium again, how does the
new internal energy of the gas compare to
the internal energy of the original system?
•
How does the new pressure of the gas
compare to the pressure of the original
system?
•
How does the new entropy of the gas
compare to the entropy of the original
system?
Studio PHY-2054C Spring 2017
3
Recitation 1/24/2017
Heat capacity and entropy
A 200 g block of copper at a temperature of 55 oC is put into an
insulated beaker of water at 20 oC. The two come to thermal
equilibrium at a temperature of about 30 oC – much closer to
the original temperature of the water than of the copper. (From
the macroscopic point of view, the specific heat of water is
about 4.2 J/g-oC while the specific heat of copper is only about
0.4 J/g-oC.) What can you conclude about the number of
degrees of freedom which share the internal energy (energy
‘bins’) in 200 g of copper compared to 200 g of water?
Studio PHY-2054C Spring 2017
4
Recitation 1/24/2017
Heat capacity and entropy
What can you conclude the about the kinetic energy associated with
moving in the x-direction (after the system has come to thermal
equilibrium) of a water molecule compared to that of a copper
atom?
Studio PHY-2054C Spring 2017
5
Recitation 1/24/2017
Reactions in ideal gases
A number N of H2 molecules and N/2 O2 molecules react to make H2O,
and all three are in the (ideal) gas phase.
A. How may H2O molecules are there?
B. If the reaction takes place at constant temperature and pressure how
does the final volume compare to the initial volume?
C. If the reaction takes place at constant temperature and volume how
does the final pressure compare to the initial pressure?
D. If the reaction takes place at constant volume in an insulating box,
what happens to the temperature?
Studio PHY-2054C Spring 2017
6
Recitation 1/24/2017
Reactions in ideal gases
The internal energy of an object at atmospheric pressure is observed
to increase. At the same time its volume changes, but pressure is
held constant. Which of the following is/are true?
A. Heat must have been added to the system.
B. If the volume increased the system did positive work on its
surroundings.
C. Since pressure is constant, enthalpy is conserved.
D. If the volume increased heat must have been added to the system.
E. If the enthalpy is constant, the volume must have decreased.
Qadded = ΔU + Wby
H = U + PV
at constant P, Wby = PΔV, and ΔH = Q
Studio PHY-2054C Spring 2017
7
Recitation 1/24/2017
Expanding gas, part II
What if the gas expands slowly
What if the gas in our insulated box expands
slowly against a piston? Work is done by the
system on the outside world:
Wby = ∫ Fdx = ∫ PdV ≈ PΔV (for small ΔV)
A. Does the internal energy go up, down, or stay
the same?
B. Does the temperature go up, down, or stay the
same
C. Does the pressure go up, down, or stay the
same?
D. Does the entropy go up, down, or stay the
same?
Studio PHY-2054C Spring 2017
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Δx
Work
outsid
ΔV
F = PA
A
Internal energy goes
Temperature goes
Pressure goes
Entropy goes
A. up
A. up
A. up
A. up
Recitation 1/24/2017
W=
Expanding gas, part II
What if the gas expands slowly
What if the gas in our insulated box expands
slowly against a piston? Work is done by the
system on the outside world:
Wby = ∫ Fdx = ∫ PdV ≈ PΔV (for small ΔV)
A. Does the internal energy go up, down, or stay
the same?
B. Does the temperature of the gas go up, down,
or stay the same
C. Does the pressure of the gas go up, down, or
stay the same?
D. Does the entropy of the gas go up, down, or
stay the same?
Δx
Work
outsid
ΔV
F = PA
A
Internal energy goes A. up
Temperature goes
A. up
Pressure goes
A. up
Entropy goes
A. up
ΔS = Q/T, but no Q flows: This is a
reversible process; if motion of
piston is reversed and it returns to
its original position, all variables
return to original values!
Studio PHY-2054C Spring 2017
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W=
Recitation 1/24/2017
Gibbs Energy: Can a change happen?
Gibbs energy
External Environment: P and T fixed.
Entropy goes up
Internal System:
Entropy changes: ΔSint,
Volume changes: ΔV
Heat transferred to
environment:
-Q
W= PΔV
Q
Suppose heat Q flows
intocan
our
system
fromintthe
which has a
Change
happen
if T(ΔS
+ ΔSenvironment,
ext ) ≥ 0
But,and
T ΔSpressure,
-ΔH the volume of our system goes up
constant temperature
ext = -Q = and
Change can happen if entropy of universe goes up, ΔSint + ΔSext ≥ 0, same as T(ΔSint + ΔSext) ≥ 0
Note ΔSext = − Q /T , so T ΔSext = − Q = − ΔHint (minus the change in enthalpy of
our internal system)
Studio PHY-2054C Spring 2017
10
Recitation 1/24/2017
Gibbs energy
Gibbs Energy: Can a change happen?
External Environment: P and T fixed.
Entropy goes up
Internal System:
Entropy changes:
ΔSint,
Volume changes: ΔV
Heat transferred to
environment:
-Q
W= PΔV
Q
Change can happen if T(ΔSint + ΔSext ) ≥ 0
can happen if T(ΔSint + ΔSext ) ≥ 0 But, T ΔSext = -Q = -ΔH
Change
But, T ΔSext = − Q = − ΔHint
So TΔSint − ΔHint ≥ 0 or(ΔHint − TΔSint) = Δ(Hint − T Sint) ≕ ΔG ≤ 0
Studio PHY-2054C Spring 2017
11
Recitation 1/24/2017
Gibbs changes
Energy: Can
a change
happen?
Spontaneous
always
reduce
Gibbs energy!
External Environment: P and T fixed.
Entropy goes up
Internal System:
Entropy changes:
ΔSint,
Volume changes: ΔV
Heat transferred to
environment:
-Q
W= PΔV
Q
Change can happen if T(ΔSint + ΔSext ) ≥ 0
can happen if T(ΔSint + ΔSext ) ≥ 0 But, T ΔSext = -Q = -ΔH
Change
But, T ΔSext = − Q = − ΔHint
So TΔSint − ΔHint ≥ 0 or(ΔHint − TΔSint) = Δ(Hint − T Sint) ≕ ΔG ≤ 0
Studio PHY-2054C Spring 2017
12
Recitation 1/24/2017
Josiah Willard Gibbs: 1839 -1903
http://en.wikipedia.org/wiki/Josiah_Willard_Gibbs
Tidbits from Wikipedia:
"In 1863, Yale awarded Gibbs the first American doctorate
in engineering."
"... for a thesis entitled "On the Form of the Teeth of Wheels
in Spur Gearing", in which he used geometrical techniques
to investigate the optimum design for gears."
" ... was praised by Albert Einstein as "the greatest mind in
American history"."
“ Gibbs, who had independent means and had yet to publish
anything, was assigned to teach graduate students exclusively
and was hired without salary.”
He was an intern before it was popular!
Studio PHY-2054C Spring 2017
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Known for
Statistical mechanics
Statistical ensemble
Gibbs entropy
Phase space
Gibbs free energy
Phase rule
Gibbs paradox
Vector calculus
Cross product
Gibbs phenomenon
Gibbs–Helmholtz equation
Gibbs–Duhem equation
Gibbs algorithm
Gibbs measure
Gibbs state
Gibbs–Thomson effect
Gibbs isotherm
Gibbs–Donnan effect
Gibbs–Marangoni effect
Gibbs lemma
Gibbs' inequality
Recitation 1/24/2017