Tag Archives: Thermodynamics

A2L Item 110

Goal: Hone the concept of heat capacity

Source: UMPERG-ctqpe210

Two thermodynamic systems are made from the same material. The specific
heat of this material is independent of temperature. The bodies have
different masses and, initially, different temperatures as shown. If the
bodies are placed in thermal contact the final equilibrium temperature
is most nearly

  1. 27 C
  2. 33 C
  3. 40 C
  4. 47 C
  5. None of the above
  6. Cannot be determined

Commentary:

Answer

(4) It is valuable to ask students how they obtained their answer. Each
of the offered answers is obtained by a common conceptual or algebraic
mistake.

A2L Item 109

Goal: Problem solving with thermal energy.

Source: UMPERG-ctqpe208

A cup of water is about 225 grams. The minimum amount of heat needed to
boil a cup of water at room temperature for tea is most nearly

  1. 10,000 cal
  2. 17,000 cal
  3. 25,000 cal
  4. 31,000 cal
  5. None of the above
  6. Cannot be determined

Commentary:

Answer

(2) This problem requires that students know the specific heat of water
and assume that the water is initially at room temperature.

A2L Item 092

Goal: Hone the concept of heat and distinguish from internal energy.

Source: UMPERG-ctqpe191

Which of the following phrases best describes heat?

  1. The total energy possessed by a body.
  2. The flow of temperature to or from a body.
  3. The amount of energy dissipated by friction.
  4. The total energy flowing between two bodies at different temperatures.
  5. The useful work that could be extracted from a body.

Commentary:

Answer

(4) Many students are confused about what heat is because the term is
not used consistently. ‘Heat’ is usually used to refer to the thermal
energy that flows into or out of a body. So ‘heat’ is not equivalent to
‘energy’ and it is inappropriate to refer to the heat possessed by a
body. Unfortunately, the redundant phrase ‘heat flow’ is often used in
texts. In addition, students frequently attribute any loss of coherent
energy to friction, which has converted the energy into ‘heat’.

A2L Item 091

Goal: Hone the concept of internal energy and heat.

Source: UMPERG-ctqpe180

Body A has a higher temperature than body B. Which of the following
statements is true?

  1. Body A will feel hotter than body B.
  2. Body A contains more energy than body B.
  3. If placed in contact with each other, energy will flow from body A to
    body B.
  4. If placed in contact with a third body having temperature greater
    than body A, body B will absorb more heat than A.
  5. More than one statement is true.

Commentary:

Answer

(3) Only statement (3) is always true. Placed in contact, heat will flow
from the higher temperature body to the other regardless of the masses
of the bodies.

The ‘feel’ of a body’s temperature depends upon the material and the
rate of heat conduction. Body A could be much smaller than body B and,
therefore, contain much less energy than body B even though at a higher
temperature. Likewise, if body B is smaller it can absorb less energy
from a third body than body A even though it has a lower temperature.

A2L Item 090

Goal: Reasoning about adiabatic expansion.

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:

Answer

(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

Goal: Reasoning about adiabatic expansion.

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

Commentary:

Answer

(1) For adiabatic expansion, pVγ is constant. Since
the volume increases, the pressure must decrease.

This result can also be reasoned by realizing that the gas won’t expand
unless the external pressure on the piston is reduced. The gas expands
because the piston moves to equalize the internal and external pressure.

A2L Item 088

Goal: Problem solving

Source: UMPERG

A quantity of gas is confined to a cylinder. The cylinder is vertical
and capped by a moveable piston of mass 2 kg and area 0.1 m2.
The gas is heated until the piston rises 20 cm. The amount of work done
by the gas is most nearly

  1. 4 J
  2. 1 J
  3. -20 J
  4. 0.4 J
  5. None of the above
  6. Cannot be determined

Commentary:

Answer

(1) This problem helps interrelate concepts from mechanics and
thermodynamics. The work can be determined from the work done against
the gravitational force.