# 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 090

Source: UMPERG

An ideal gas is allowed to expand slowly. The system is thermally
isolated.

Which statement regarding the final temperature is true?

1. T’ < T
2. T’ = T
3. T’ > T
4. Not enough information

### Commentary:

(1) For adiabatic expansion, TV(γ-1) is constant.
Since the volume increases, the temperature must decrease.

This result can be reasoned by considering the fact that work is done by
the gas. Since there is no heat transfer, the internal energy must
decrease. Since the internal energy of a perfect gas depends only upon
temperature, the temperature must decrease.

# A2L Item 089

Source: UMPERG

An ideal gas is allowed to expand slowly. The system is thermally
isolated.

Which statement regarding the final pressure is true?

1. P’ < P
2. P’ = P
3. P’ > P
4. Not enough information