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:
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:
(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
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
(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.
Goal: Link representations
Source: UMPERG-ctqpe196
A vertical cylinder with a movable cap is cooled. The process
corresponding to this is
(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?
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) 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
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…
(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.
Goal: Reasoning about temperature.
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) Students may erroneously apply prior knowledge that gas cools as it
expands. Some will likely think that the answer cannot be determined
without more information.
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:
(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.
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?
(4) If V is linearly related to T the perfect gas law implies that the
pressure is constant.
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 work is done ON the system. Since the path on a V-T diagram
is a straight line, the process is isobaric.
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.