The diagram shows the pressure \(p\) and volume \(V\) relationship for one cycle of operation of an engine.

Which of the labelled parts of the cycle identify isobaric changes and adiabatic changes of state?

D

The graph below represents the variation with time of the displacement of an oscillating particle.

The motion of the object is

A.     over damped.

B.     critically damped.

C.     lightly damped.

D.     not damped.

C

The graph shows the variation of pressure P with volume V for a gas undergoing an adiabatic expansion.

Which of the following areas correctly identifies the work done by the gas?

A. X
B. X+Z
C. X−Z
D. Z

B

The work done on a gas is the total area under a P-V graph. Many candidates incorrectly opted for response A.

Microwave ovens cause the water molecules in food to resonate. Water molecules have a natural frequency of vibration f. In order to heat the food most effectively, the frequency of the microwaves should have a value

A. less than f.
B. equal to f.
C. greater than f.
D. as large as possible.

B

Which of the following can be deduced from the second law of thermodynamics?

A. Thermal energy cannot spontaneously transfer from a low temperature region to a high temperature region.
B. Thermal energy cannot spontaneously transfer from a high temperature region to a low temperature region.
C. The entropy of an isolated system always decreases with time.
D. The entropy of an isolated system is the measure of the internal energy of the system.

A

Which of the following is equivalent to the principle of energy conservation?

A. Newton’s first law
B. The first law of thermodynamics
C. Newton’s second law
D. The second law of thermodynamics

B

An ideal gas undergoes the thermodynamic changes represented in the P –V diagram below (P→Q→R→P).

Which of the following is the net work done by the gas in a cycle?

A. 4.5 × 10⁵ J
B. 3.0 × 10⁵ J
C. 1.0 × 10⁵ J
D. Zero

C

Two oscillators X and Y are undergoing forced oscillations each at a frequency close to the natural frequency of each oscillator. The graph shows the variation of amplitude with forcing frequency for each oscillator.

Which of the following correctly identifies the system that has the greater amount of damping and the
greater natural frequency of oscillation?

D

This question elicited a number of comments on the G2s and the statistics showed that the topic had been sufficiently understood by only the better candidates. These two systems were clearly not identical – otherwise they would have had the same y-intercept. Y had a blunter peak which was visibly to the right of X’s peak, making D the best answer.

A fixed mass of gas is compressed in a very short period of time. Which of the following describes this process?

A. Adiabatic
B. Isobaric
C. Isochoric (isovolumetric)
D. Isothermal

A

The entropy of a system is a measure of the system’s

A. total energy only.
B. degree of disorder and total energy.
C. degree of disorder only.
D. degree of disorder and average kinetic energy.

C

A system consists of a refrigerator with its door open operating in a thermally insulated room. What are the change in the entropy of the system and the change in temperature of the room?

D

The fridge is switched on and is within a closed system. This means that, as the fridge is consuming energy, the room will rise in temperature.

An ideal gas expands isothermally from a state X to a new state of volume \(V\). The work done by the gas is \(W\). Which of the following is correct for an adiabatic expansion of the gas from state X to a new state of volume \(V\)?

D

Which of the following correctly describes the entropy changes of the water molecules and the universe when a sample of water freezes?

B

The pressure–volume (P–V) graph shows an adiabatic compression of a fixed mass of an ideal gas.

Which of the following correctly describes what happens to the temperature and the internal energy of the gas during the compression?

D

Water in a container freezes. Which of the following correctly describes the change in entropy of the water and its surroundings?

B

An isolated system consists of a block of ice floating in a glass of water. The ice melts completely at constant temperature. Which of the following identifies the change in internal energy of the system and the change in entropy of the system?

A

There were a number of comments on this question from the teachers. In this situation the slight change in volume of the water/ice can be taken as negligible and it must be assumed that the water is not at 0^oC, otherwise no melting would occur. The statistics showed that the better candidates understood this, choosing A as the best response.

An ideal gas expands adiabatically. What energy change is true for the gas?

A. It gains thermal energy from the surroundings
B. It loses thermal energy to the surroundings
C. Its internal energy increases
D. Its internal energy decreases

D

An ideal gas undergoes adiabatic expansion from state X to a new state of volume V. During this process the work done by the gas is W. What is the change in internal energy and the work done in an isothermal expansion of this gas from X to V?

A

The entropy of a system

A. will decrease if the system’s temperature is increased.

B. is related to the degree of disorder in the system.

C. must always increase.

D. is always conserved.

B

A positive amount of thermal energy \(Q\) is transferred to an ideal gas from its surroundings. The internal energy of the gas increases and the gas does a positive amount of work \(W\) on its surroundings. The change of state of the gas is

A.     isochoric (isovolumetic).

B.     isobaric.

C.     isothermal.

D.     adiabatic.

B

In the P–V diagram below, which line could represent an adiabatic change for an ideal gas?

C

A block of ice at 0°C is placed on a surface and allowed to melt completely to give water at 0°C. During this process the entropy of the

A. molecules in the block has decreased.

B. surroundings has increased.

C. universe has increased.

D. universe has decreased.

C

The graph below shows the variation of the pressure \(p\) with volume \(V\) of an ideal gas during one cycle of an engine.

Which of the following correctly names the thermodynamic process associated with the parts \({\text{Y}} \to {\text{Z}}\) and \({\text{Z}} \to {\text{X}}\) of the cycle?

A

Which of the following statements is consistent with the second law of thermodynamics?

A. Thermal energy can ow by itself from a cold to a hot body.
B. A heat engine can be 100 % ef cient.
C. In natural processes, total entropy tends to increase.
D. The entropy in every closed system is constant.

C

Which process will increase the entropy of the local surroundings?

A. The melting of a block of ice

B. Evaporation of water vapour

C. The isothermal expansion of a gas

D. The adiabatic expansion of a gas

C

There is evidence of much guessing in this question and it elicited a few adverse comments from the teachers. But both A and B are logically equivalent so must be wrong. As an adiabatic expansion involves no thermal exchange with the surroundings, this will not affect the entropy of the local surroundings. Hence C must be correct by elimination.

The following statement refers to question 11 and question 12.

A gas is contained in a thermally insulated cylinder by a freely moving piston. The volume of the gas is increased reversibly by moving the piston.

Which term identifies the change of state of the gas?

A. Isobaric
B. Isochoric
C. Isothermal
D. Adiabatic

D

The graph shows how the volume of a system varies with pressure during a cycle ABCA.

What is the work done in joules during the change AB?

A.     \(15 \times {10^5}\)

B.     \(9.0 \times {10^5}\)

C.     \(4.5 \times {10^5}\)

D.     0

A

The diagram shows a P–V cycle for a particular gas.

In which of the following changes is no work being done?

A. 1 → 2
B. 1 → 2 → 3
C. 1 → 2 → 3 → 4
D. 2 → 3

D

The graph shows the variation of pressure P with volume V of an ideal gas during a thermodynamic cycle.

During which stages is work done on the gas and work done by the gas?

D

Which of the following gives the conditions for maximum amplitude in forced, but damped, oscillations?

D

The following statement refers to question 11 and question 12.

A gas is contained in a thermally insulated cylinder by a freely moving piston. The volume of the gas is increased reversibly by moving the piston.

Which of the following gives the correct entropy change of the gas and the surroundings?

D

A piece of ice melts at constant temperature. Which of the following gives the correct change in the entropy of the water molecules and that of the surroundings?

A