# A2L Item 195

Goal: Reasoning with thermodynamics

Source: ctqpe214 A
system consisting of a quantity of ideal gas has the two isotherms
shown. The system, initially at state C, can be taken along path CA to
final state A or along path CB to state B.

Which of the following is true:

1. QCA < QCB
2. QCA = QCB
3. QCA > QCB
4. Not enough information

### Commentary:

(1) Since the internal energy of an ideal gas depends only on
temperature, states A and B have the same internal energy. Along path CB
the system does work requiring more heat to be added than along path CA.

# A2L Item 194

Goal: Reasoning with thermodynamics

Source: UMPERG-ctqpe212 The
two curves shown are isotherms. A system is taken from state A to state
B along the T2 isotherm. State C has the volume of state A
and the pressure of state B.

Which of the following is true:

1. QAB = 0
2. QAB = ΔEAB
3. QAB = -WAB
4. QAB = QCA-QCB
5. Not enough information

### Commentary:

(5) This is the only answer that is definitely correct. Students
will likely assume that the system is an ideal gas. Many will choose #3
and this should engender a discussion of the sign of work. Physicists
use the convention that positive work is that done BY the system.
Chemists frequently use the opposite convention.

The one choice giving students the most reasoning difficulty is #4. A
reasoning path that eliminates that choice is as follows. Q(AB) is
positive: gas does positive work on surroundings, so heat has to be
added to keep energy the same. Q(CA) is positive: no work is done, so
heat has to be added to raise the temperature. Q (CB) is positive: heat
must be added to expand the gas and still maintain constant pressure. So
Q(CB) [constant pressure] > Q(CA) [constant volume]; Q(CA) – Q(CB) < 0
cannot equal Q(AB) > 0

# A2L Item 193

Goal: Problem solving in thermodynamics

Source: UMPERG-ctqpe198 An
amount of an ideal gas is taken around the process shown.The amount of
heat extracted during process BC is

1. 10 J
2. 20 J
3. 15 J
4. 45 J
5. 60 J
6. none of the above
7. cannot be determined

### Commentary:

(4) Since no work is done the change in internal energy must be
due to heat extraction. Some students may think that the answer cannot
be determined because they do not know the number of moles. These are
likely thinking that they need to find the temperature at each state to

# A2L Item 192

Source: UMPERG-ctqpe196  A vertical cylinder with a movable cap is cooled. The process
corresponding to this is

1. C-B
2. A-B
3. A-C
4. C-A
5. is not shown

### Commentary:

(4) Interpreting process diagrams is a very important skill for
students. good followup questions include; Is work done during this
process? … by or on the gas? How does the temperature at A compare to
that at C? How much heat was extracted during this process?

# A2L Item 191

Goal: Reason with internal energy

Source: UMPERG-ctqpe194var An
amount of an ideal gas is taken around the process shown. Which of the
following statements about the internal energy of the states is true?

1. The internal energy of state B is twice that of state C.
2. The internal energy of state B is equal to that of A and C combined.
3. The internal energy of state A is half that of state C.
4. The internal energy of state B is less than the internal energy of state
A.
5. none of the above
6. cannot be determined

### Commentary:

(1) Students need to know only that the internal energy depends
upon the product of p and V. Alternatively, they can reason that,
according to the Ideal Gas Law, this product is proportional to the
temperature and the temperature determines the internal energy

# A2L Item 190

Goal: Hone the concept of work for a thermodynamic system

Source: UMPERG-ctqpe190 An
ideal gas is taken around the process shown. The net work done
on the gas is most nearly…

1. 20 J
2. -30 J
3. 15 J
4. -10 J
5. none of the above
6. cannot be determined

### Commentary:

(4) The work done ON the system is the negative of the area of
the triangle. Students selecting answer #1 or #3 need to be sensitized
to the difference between work done on the gas versus by the gas.

# A2L Item 115

Source: UMPERG-ctqpe186 Two moles of an ideal gas fill a volume of 10 liters with a pressure of
2.4 atm. The gas is thermally insulated from the surroundings. A
membrane is broken which allows the gas to expand into the new volume
which is 3 times as large as the old volume. The new temperature is …

1. The same as before.
2. Lower than before.
3. Higher than before.
4. Cannot be determined.

### Commentary:

(1) Students may erroneously apply prior knowledge that gas cools as it
expands. Some will likely think that the answer cannot be determined

# A2L Item 114

Goal: Problem solving with the ideal gas law

Source: UMPERG-ctqpe184 Two moles of an ideal gas fill volume V = 10 liters at pressure P = 2.4
atm. The gas is thermally insulated from the surroundings. A membrane
is broken which allows the gas to expand into the new volume which is 3
times as large as the old volume. The new pressure is:

1. .4 atm
2. .8 atm
3. 1.2 atm
4. 1.6 atm
5. 2.4 atm
6. None of the above
7. Cannot be determined

### Commentary:

(2) Some students may wonder about the applicability of the ideal gas
law for free expansion. Some may respond (7) thinking that since gas
cools as it expands, they do not know what the final temperature is and
cannot, therefore, use the ideal gas law.

# A2L Item 113

Goal: Hone reading graphical depictions of thermodynamic cycles.

Source: UMPERG-ctqpe216

A quantity of ideal gas undergoes a thermodynamic process. Which curve
represents an isobaric path? ### Commentary:

(4) If V is linearly related to T the perfect gas law implies that the
pressure is constant.

# A2L Item 112

Goal: Hone the concept of work on a gas

Source: UMPERG-ctqpe220 One mole of an ideal monatomic gas is taken around the cycle shown.

The work done on the system during the process B to C is

1. Positive
2. Negative
3. No work is done on the system
4. Cannot be determined