Entropy
Contributions by:
John L. Falconer & Will Medlin
Department of Chemical and Biological Engineering
University of Colorado
Boulder, CO 80309

0424
Supported by the National Science Foundation
You have 4 balls: red, green blue, and yellow. You
distribute them all into two cans. How many different
ways can you do this?
A.
4
B.
8
C.
12
D.
16
E.
None of the above
A gas is compressed isothermally. The entropy of the
surroundings ________.
A.
increases
B.
decreases
C.
remains the same.
D.
Insufficient information.
What external pressure should be used in the W
EC
term when calculating the entropy change for
isothermal compression of an ideal gas?
A.
A constant external pressure
B.
An external pressure that is always equal to the
system pressure
C.
Either (A) or (B)
D.
Neither (A) or (B)
Air flows steadily at constant pressure through a pipe
that is heated by a furnace. As air flows through the
pipe, the entropy of the air _______.
A.
increases
B.
remains the same
C.
decreases
D.
Insufficient information
S
i
S
o
Which of the following systems will have the largest
entropy change when the blue partition is removed?
The ideal gases are initially at 1 atm.
N
2
Vacuum
N
2
N
2
N
2
O
2
Vacuum
O
2
A
B
C
D
Which of the following systems will have the largest
entropy change when the blue partition is removed?
The gases are ideal.
2
atm
N
2
1
atm
O
2
3
atm
N
2
3
atm
N
2
2
atm
N
2
Vacuum
Vacuum
1
atm
O
2
A
B
C
D
W
hen the blue partition is removed between the two
ideal gases below, the change is entropy is
D
S
=
3Rln(2). What
is most correct expression for
D
G?
1
atm
1
mol
Ar
2
atm
2
mol
O
2
A.
∆H

3RTln(2)
B.
∆H

3Rln(2
)
C.

3RTln
(2)
D.
3RTln
(2)
E.
∆H+3RTln(2
)
An ideal gas undergoes two irreversible processes
between state 1 and state 2. For process A, 100 kJ of
work was done
by
the gas. For process B, 200 kJ of
work was done
by
the gas.
Which process has the larger entropy change for the
gas?
A.
Process A
B.
Process B
C.
Both process have the same change in entropy of
the gas
1
2
100 kJ
1
2
200 kJ
A gallon of hot water is mixed with a gallon of cold
water in a perfectly insulated container. When the
waters are mixed, the entropy _______.
A.
increases
B.
decreases
C.
remains the same
D.
Insufficient information
1.0 mol of hot water mixes adiabatically with 1.0 mol of
cold water. The entropy change of the cold water is
0.21 J/(
mol
•
K
). The
entropy
change of the hot water is
_______.
A.
positive
B.
<

0.21 J/(
mol
•K
)
C.
< 0.21 J/(
mol
•
K
)
D.
> 0.21 J/(
mol
•
K
)
E.
>

0.21 J/(
mol
•
K
)
Δ
S =
0.21 J/(
mol
•
K
)
Δ
S = ?
Consider a completely insulated system. A reaction
takes place inside the system. Therefore the system’s
entropy
__________.
A.
remains the same since Q = 0
B.
increases
C.
decreases
D.
Need more information
Insulation
System
An
endothermic
reaction takes place in
a
completely
insulated, closed container of fixed volume.
What happens to the entropy of
system?
A. Increases
B. Decreases
C. Does not change
Insulation
System
An
exothermic
reaction takes place in
a
completely
insulated, closed container of fixed volume.
What happens to the entropy of
system?
A. Increases
B. Decreases
C. Does not change
Insulation
System
You raise the pressure of a gas at constant
temperature in a closed, adiabatic system.
The
entropy
of the gas ___________.
A.
does not change since temperature is constant
B.
does not change since there is no heat transfer
C.
increases
D.
decreases
This picture shows a DNA molecule on a surface with
vertical pillars on half the surface. The DNA will
_______.
A.
move into the pillars more
B.
move out onto the open area
C.
stay where it is
Container A has 2 kg of water, and container B has 1
kg of water. Both containers are initially at 50
o
C. To
each container, 20
kJ of heat is
added. Which
container has
the
greater
total (NOT per kg water)
entropy
change?
A.
A
B.
B
C.
Same entropy change for both
D.
Need more information
1
kg water
at 50
o
C
2
kg water
at 50
o
C
A
B
Q
A
= 20 kJ
Q
B
= 20 kJ
In these piston

cylinder systems, when the red stop is
removed, the ideal gas expands, and the piston moves
until it hits the black stopper. Each system is adiabatic
and starts at 10
atm
and 25
°
C.
Which has the
largest
entropy change?
A.
A
B.
B
C.
C
D.
All the same
1
8
2 kg
Vacuum
Gas
Piston
Block
A
1 kg
Vacuum
Gas
B
Vacuum
Gas
C
For which does entropy increase?
A.
Constant V
B.
Constant P
C.
Both
D.
Neither
Constant
V
Constant
P
Which system has the
highest
entropy if one mole of
the same ideal gas is in each piston

cylinder?
A.
A
B.
B
C.
Both have the
same entropy
2
atm
50
°
C
10
atm
50
°
C
A
B
Which system has the
greatest
entropy change if
10
mol
N
2
are in each piston

cylinder, which are
initially at 100
°
C. Both processes are reversible.
A.
A
B.
B
C.
Same change for
both
A
B
W
A
= 0 kJ
W
B
= 50 kJ
Q
A
=12 kJ
Q
B
=10 kJ
You lower the pressure of a gas at constant
temperature in
a closed, adiabatic
system.
The
entropy
of the
gas ___________.
A.
does not change since temperature is constant
B.
does not change since there is no heat transfer
C.
increases
D.
decreases
Which
is the best approximation to a
constant
pressure
process for a gas on
a H

S diagram?
H
S
A
H
S
B
H
S
C
H
S
D
A
B
C
D
E
Which is the correct plot of entropy of the system (S)
vs. mole fraction of component i (
y
i
) for a binary
mixture of ideal gases?
y
i
S
y
i
S
y
i
S
y
i
S
y
i
S
A gas goes from states A to B in a reversible adiabatic
process. It then goes from B back to A by a different
pathway that is irreversible and not adiabatic. The
entropy change for the gas for the irreversible pathway
is _______ zero.
A.
greater than
B.
less than
C.
equal to
V
P
A
B
Rev.
Irrev
.
Enthalpy
Pressure
A
B
C
D
E
Which line most likely corresponds to a constant
entropy process?
One mol of CH
4
at 1 bar and 50
°
C is mixed with 1 mol
of O
2
at 1 bar and 50
°
C. The final mixture is at 2 bar
and 50
°
C. Assume ideal gases.
The Gibbs free energy change is ___________.
A.
positive
B.
negative
C.
zero
Which is the most correct plot of Gibbs free energy
versus temperature for a single component?
T(K)
T(K)
A
Gibbs (J/g)
T

sat
0
B
Gibbs (J/g
)
T

sat
0
C
Gibbs (J/g
)
T(K)
T

sat
0
D
Gibbs (J/g
)
T(K)
T

sat
0
E
Gibbs (J/g
)
T(K)
T

sat
0
Which is the most correct plot of
Gibb’s
free
energy versus pressure
for a single component?
P(
atm
)
P(
atm
)
A
Gibbs (J/g)
P

sat
0
B
Gibbs (J/g
)
P

sat
0
C
Gibbs (J/g
)
P(
atm
)
P

sat
0
D
Gibbs (J/g
)
P(
atm
)
P

sat
0
E
Gibbs (J/g
)
P(
atm
)
P

sat
0
Two of these plots represent enthalpy and entropy vs.
temperature for a pure component going from liquid to
vapor. Identify the correct axes labels.
A.
Y = S ; Z = H
B.
W = S ; X = H
C.
W = H ; X = S
D.
Z = H ; X = S
E.
R = H ;Z = S
T(K)
Z
T(K)
X
T(K)
Y
T(K)
R
T(K)
W
For an ideal gas, if the pressure is increased while
keeping the entropy constant, the enthalpy ________.
A.
increases
B.
decreases
C.
remains the same
D.
Need more information.
Two different paths can be used for a process that
changes the state of a fluid from 300 K and 1 bar to
500 K and 9 bar. Path A is adiabatic and reversible,
and Path B is non

adiabatic and irreversible. Which of
the following statements is
true
?
A.
The change in entropy of the fluid will be greater for
path A
B.
The change in entropy of the fluid will be greater for
path B
C.
Both paths will have the same change in entropy of the
fluid, but the change will be positive
D.
The compression in path A will require less work
Hydrogen storage often involves the sorption of
hydrogen from the gas phase into a solid material,
where it can be stored more densely. For the
adsorption/desorption process involved in H
2
storage,
which process should be run at a lower temperature?
A.
Adsorption of hydrogen into material.
B.
Desorption of hydrogen from material.
C.
It does not matter.
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