Tag Archives: Graphing

A2L Item 260

Goal: Interrelate representations of kinematical quantities

Source: CT151.2-10

An object’s motion is described by the graph above. The displacement
of the object during the entire 16 seconds is most nearly…

  1. 200 meters
  2. 250 meters
  3. 300 meters
  4. 350 meters
  5. 400 meters
  6. 450 meters
  7. Cannot be determined

Commentary:

Answer

(7) Students have difficulty reading graphs and finding areas.

A2L Item 259

Goal: Interrelate representations of kinematical quantities

Source: CT151.2-8

An object’s motion is described by the graph above. The position of the
object at t = 9 seconds is most nearly…

  1. 0 meters
  2. 200 meters
  3. 300 meters
  4. 400 meters
  5. 500 meters
  6. Cannot be determined

Commentary:

Answer

(6) This problem is primarily to determine if students appreciate the
information available from a graph. Many students will determine the
displacement forgetting that the initial position is unknown.

A2L Item 210

Goal: Relate representations

Source: 283-342 Graph Ex(x)

We have a charge configuration
(shown at the right). Which graph is the plot of Ex(x), the
x component of the electric field, as you move along the
x-axis?


Commentary:

Answer

(6) Students should recognize that the field goes singular at the
charges. The only graphs doing that, #1 and #4, are eliminated because
the x-component of the field must be negative everywhere between the two
charges. Have students sketch the graph.

A2L Item 209

Goal: Translate among representations

Source: 283-341 graph Ex(y)

We have a charge configuration
(shown at the right). Which graph below resembles the plot of the x
component
of the electric field, Ex(y), as you move
along the y-axis?


Commentary:

Answer

(6) The correct graph looks like the negative of graph #5. Some students
pick #5 thinking that the magnitude of the field is desired.

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:

Answer

(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 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:

Answer

(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 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:

Answer

(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
answer the question.

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:

Answer

(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 192

Goal: Link representations

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:

Answer

(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 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:

Answer

(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.