B.4 Thermodynamics
Practice exam-style IB Physics questions for Thermodynamics, aligned with the syllabus and grouped by topic.
Question 1
A fixed mass of gas in a cylinder is chosen as the system. It receives 120 J by heating and does 45 J of work on the piston. What is the change in internal energy of the gas?
A.
−165 J
B.
165 J
C.
−75 J
D.
75 J
Question 2
A gas at constant pressure expands from 2.0 × 10⁻³ m³ to 5.0 × 10⁻³ m³. The work done by the gas is positive. What must be true of the process?
A.
The system boundary moves inwards and ΔV is positive.
B.
The system boundary moves outwards and ΔV is negative.
C.
The system boundary is fixed and ΔV is zero.
D.
The system boundary moves outwards and ΔV is positive.
Question 3
Entropy is best described as a thermodynamic quantity related to
A.
the pressure exerted by particles on a container wall only.
B.
the average speed of particles only.
C.
the number of microscopic arrangements compatible with a macroscopic state.
D.
the total mass of the particles in a closed system.
Question 4
The Kelvin form of the second law states that a cyclic heat engine cannot
A.
reject energy to a cold reservoir during each cycle.
B.
convert all energy taken from a single hot reservoir into work.
C.
have a working substance that returns to its initial state.
D.
transfer energy from a cold body to a hot body when work is supplied.
Question 5
A gas expands freely into a vacuum inside a rigid insulated container. The process is irreversible because
A.
energy is not conserved during the expansion.
B.
the temperature of every particle must become zero.
C.
the gas becomes distributed among more possible microscopic arrangements.
D.
the gas must do boundary work on the container walls.
Question 6
A closed system receives 850 J by heating. At the same time, 320 J of work is done on the system.
State the sign of W for the system.
[1]
Calculate the change in internal energy of the system.
[1]
Question 7
Define entropy in terms of microscopic arrangements.
[1]
State the SI unit of entropy.
[1]
Question 8
State the second law of thermodynamics in:
Clausius form.
[1]
Kelvin form.
[1]
entropy form for an isolated system.
[1]
Question 9
The temperature of 0.20 mol of a monatomic ideal gas increases by 40 K. What is the increase in internal energy of the gas?
A.
2.0 × 10² J
B.
6.6 × 10¹ J
C.
1.0 × 10² J
D.
5.0 × 10² J
Question 10
A system receives 600 J of energy reversibly by heating at a constant temperature of 300 K. What is its entropy change?
A.
−2.0 J K⁻¹
B.
2.0 J K⁻¹
C.
0.50 J K⁻¹
D.
9.0 × 10⁴ J K⁻¹
Question 11
Water freezes in a freezer. The entropy of the water decreases. This does not violate the second law because
A.
the second law applies only to ideal gases.
B.
entropy is not defined for solids.
C.
the water becomes an isolated system when it freezes.
D.
the freezer and its surroundings have an entropy increase at least as large.
Question 12
An ideal gas undergoes an isothermal expansion. What is true for the gas?
A.
ΔU = 0 and Q = W.
B.
Q = 0 and ΔU = −W.
C.
W = 0 and Q = ΔU.
D.
P is constant and W = PΔV.
Question 13
A closed loop on a P–V diagram is traversed clockwise. What does the area enclosed by the loop represent?
A.
The net increase in internal energy in one cycle.
B.
The thermal energy rejected to the cold reservoir only.
C.
The entropy decrease of the gas in one cycle.
D.
The net work done by the gas in one cycle.
Question 14
A heat engine takes 2.5 kJ from a hot reservoir and rejects 1.6 kJ to a cold reservoir per cycle. What is its efficiency?
A.
0.56
B.
1.56
C.
0.36
D.
0.64
Question 15
A Carnot engine operates between reservoirs at 600 K and 300 K. What is the maximum possible efficiency?
A.
0.33
B.
0.67
C.
2.0
D.
0.50
Question 16
A gas expands at a constant pressure of 1.8 × 10⁵ Pa from 4.0 × 10⁻³ m³ to 9.0 × 10⁻³ m³.
Calculate the work done by the gas.
[1]
State whether this work is positive or negative.
[1]
Question 17
A sample of 0.75 mol of monatomic ideal gas is cooled from 420 K to 360 K.
Calculate the change in internal energy of the gas.
[1]
State whether the answer depends on the path followed between the two temperatures.
[1]
Give a reason for your answer to (b).
[1]
Question 18
A block melts reversibly at a constant temperature of 330 K while receiving 1.65 × 10⁴ J by heating.
Calculate the entropy change of the block.
[1]
State the sign of the entropy change of the surroundings.
[1]
Question 19
A simple model has 6 distinguishable counters. Each counter may be in the left or right half of a box.
Determine the total number of microstates.
[1]
Determine the number of microstates for the macrostate with exactly 3 counters in the left half.
[1]
State why this macrostate is more likely than all 6 counters being in the left half.
[1]
Question 20
Two different gases at the same temperature are separated by a removable partition in an insulated rigid container. The partition is removed and the gases mix.
State the change in total entropy of the gases.
[1]
Explain why the reverse process is not observed.
[1]
Question 21
A plant grows ordered structures using energy from sunlight.
State why the entropy of the plant itself may decrease.
[1]
Explain why this does not contradict the second law.
[1]
Question 22
A gas undergoes an anticlockwise cycle on a P–V diagram.
State the sign of the net work done by the gas.
[1]
Explain what the enclosed area represents.
[1]
State the net change in internal energy for the cycle.
[1]
Question 23
A fixed mass of gas expands along the path shown on the P–V graph.
Determine the approximate work done by the gas during the expansion.
[1]
State why using W = PΔV with the initial pressure would be inappropriate.
[1]
Suggest how the estimate of work could be improved from the graph.
[1]
Question 24
A P–V graph shows four labelled processes for the same fixed mass of ideal gas.
Identify the isovolumetric process.
[1]
Identify the isobaric process.
[1]
Identify the isothermal expansion.
[1]
State which of the four processes has zero boundary work.
[1]
Question 25
An isothermal and an adiabatic curve pass through the same state on a P–V diagram for a monatomic ideal gas. For the same small expansion from that state, the adiabatic curve is
A.
vertical, because volume is constant in an adiabatic process.
B.
less steep, because the gas is heated during adiabatic expansion.
C.
steeper, because the gas cools during adiabatic expansion.
D.
horizontal, because pressure is constant in an adiabatic process.
Question 26
For a monatomic ideal gas, the pressure is P₁ and volume is V₁. It expands adiabatically to volume 2V₁. What is the final pressure?
A.
P₁/2
B.
2^(5/3)P₁
C.
P₁/2^(5/3)
D.
2P₁/5
Question 27
A model system has Ω₁ microstates initially and Ω₂ = 8Ω₁ finally. What is the entropy change?
A.
kB/8
B.
8kB ln Ω₁
C.
kB ln 8
D.
−kB ln 8
Question 28
A real engine operates between the same two reservoirs as a Carnot engine. Its efficiency is lower than the Carnot value mainly because real engines involve
A.
a working substance that always remains at constant volume.
B.
irreversible processes such as friction and finite-temperature heat transfer.
C.
a cold reservoir at absolute zero.
D.
zero entropy change of the universe in every process.
Question 29
A gas process is shown on a P–V diagram.
Identify the process A→B.
[1]
State the work done during A→B.
[1]
Identify the process B→C.
[1]
State the relation between P and V for B→C if the gas is ideal and the temperature is constant.
[1]
Question 30
A monatomic ideal gas at pressure 2.4 × 10⁵ Pa and volume 1.5 × 10⁻³ m³ undergoes an adiabatic expansion to volume 3.0 × 10⁻³ m³.
State the adiabatic relation for this gas.
[1]
Calculate the final pressure.
[1]
State whether the temperature increases or decreases.
[1]
Question 31
A heat engine takes 4.0 kJ from a hot reservoir and rejects 2.7 kJ to a cold reservoir in each cycle.
Calculate the net work output per cycle.
[1]
Calculate the efficiency.
[1]
State the change in internal energy of the working gas over one complete cycle.
[1]
Question 32
A power station heat engine has a hot reservoir at 820 K and a cold reservoir at 290 K.
Calculate the Carnot efficiency.
[1]
State one practical reason why the actual efficiency is lower.
[1]
Question 33
Compare an isothermal expansion and an adiabatic expansion of the same monatomic ideal gas, starting from the same state.
State the value of ΔU for the isothermal expansion.
[1]
State the value of Q for the adiabatic expansion.
[1]
State which curve is steeper on a P–V diagram.
[1]
Explain the reason for the difference in steepness.
[1]
Question 34
The table gives measurements for a monatomic ideal gas during a process.
| State | T / K | P / Pa | V / m^3 | n / mol | P–V path |
|---|---|---|---|---|---|
| Initial | 300 | 1.25×10^5 | 1.00×10^-2 | 0.500 | constant P |
| Final | 600 | 1.25×10^5 | 2.00×10^-2 | 0.500 | constant P |
Use the data to determine the change in internal energy.
[1]
Use the P–V data to determine the work done by the gas.
[1]
Hence determine the energy supplied to the gas by heating.
[1]
State whether the process is adiabatic.
[1]
Question 35
A model uses 8 distinguishable particles that may be in the left or right half of a box. The table shows the number of microstates for different macrostates.
| Particles on left | Microstates |
|---|---|
| 0 | 1 |
| 1 | 8 |
| 2 | 28 |
| 3 | 56 |
| 4 | 70 |
| 5 | 56 |
| 6 | 28 |
| 7 | 8 |
| 8 | 1 |
Identify the most probable macrostate.
[1]
Determine the entropy difference between the macrostate with 4 particles on the left and the macrostate with all particles on the left, in terms of kB.
[1]
Explain why the gas is not expected to remain with all particles on the left.
[1]
Question 36
A gas engine cycle is shown on a P–V diagram.
Determine whether the net work is done by the gas or on the gas.
[1]
Estimate the net work per cycle.
[1]
If the energy taken from the hot reservoir per cycle is given in the data, determine the efficiency.
[1]
State the change in internal energy over one cycle.
[1]
Question 37
The table shows the energy input and useful output for three heat-engine cycles operating with the same working gas.
| Cycle | Energy input / kJ | Useful work output / kJ |
|---|---|---|
| Cycle A | 250 | 90 |
| Cycle B | 300 | 120 |
| Cycle C | 500 | 140 |
Calculate the efficiency of each cycle.
[1]
Identify the cycle with the greatest efficiency.
[1]
Suggest why the greatest work output is not necessarily the greatest efficiency.
[1]
Question 38
The table gives entropy changes when water freezes in a freezer compartment and energy is transferred to the surroundings.
| Subsystem | Entropy change / J K⁻¹ |
|---|---|
| Water | −18 |
| Surroundings | +24 |
Identify the subsystem with a negative entropy change.
[1]
Determine the total entropy change for water plus surroundings.
[1]
State whether the overall process is allowed by the second law.
[1]
Explain your answer to (c).
[1]
Question 39
A proposal claims that an engine operating between 500 K and 300 K can have an efficiency of 55%.
Calculate the Carnot efficiency for these reservoir temperatures.
[1]
Evaluate the claim.
[1]
Question 40
Measurements for a rapidly compressed monatomic ideal gas are plotted as ln P against ln V.
State the expected gradient for an adiabatic process.
[1]
Use the graph to determine the experimental gradient.
[1]
Evaluate whether the data support an adiabatic model.
[1]
Question 41
A graph shows measured efficiencies of several engines operating with the same cold reservoir but different hot-reservoir temperatures. The Carnot limit is also shown.
Read the Carnot efficiency at the highest hot-reservoir temperature shown.
[1]
Determine whether any measured engine exceeds the Carnot limit.
[1]
Explain the significance of a measured point above the Carnot line.
[1]
Suggest one reason measured efficiencies are below the Carnot line.
[1]
Question 42
A monatomic ideal gas in a cylinder is compressed rapidly by a piston. The cylinder is well insulated.
State the first law of thermodynamics using the Clausius sign convention, defining each term.
[1]
Explain why the temperature of the gas increases during the rapid insulated compression.
[1]
Question 43
A fixed mass of monatomic ideal gas may undergo isovolumetric, isobaric, isothermal or adiabatic processes.
Identify the P–V graph shape for an isovolumetric and for an isobaric process.
[1]
Explain the energy transfers and internal-energy changes for isothermal and adiabatic expansions.
[1]
Question 44
A proposed cyclic device is described by the energy transfers shown in the diagram.
| Quantity | Value |
|---|---|
| Hot reservoir temperature / K | 600 |
| Cold reservoir temperature / K | 300 |
| Energy absorbed per cycle / J | 800 |
| Energy rejected per cycle / J | 300 |
Determine the net work output per cycle from the data.
[1]
Calculate the efficiency of the proposed device.
[1]
Compare the efficiency with the Carnot efficiency for the stated reservoir temperatures.
[1]
Evaluate whether the device is physically possible.
[1]
Question 45
A student estimates work from a P–V graph for a gas expansion but uses only the rectangular area visible within the plotted grid. The graph axes do not start at zero.
Describe how work done by a gas is obtained from a P–V graph.
[1]
Evaluate the student’s method and explain how a correct estimate should be made.
[1]
Question 46
A gas expands isothermally into a larger volume while in thermal contact with a reservoir.
Outline the microscopic meaning of entropy using S = kB ln Ω.
[1]
Discuss how the entropy increase of the gas can be described both microscopically and macroscopically during the isothermal expansion.
[1]
Question 47
The second law may be expressed in Clausius form, Kelvin form and entropy form.
State the Clausius and Kelvin forms of the second law.
[1]
Compare these statements with the entropy form of the second law for reversible and irreversible processes in isolated systems.
[1]
Question 48
A proposed engine cycle for a monatomic ideal gas consists of an isovolumetric heating stage, an adiabatic expansion stage and an isobaric compression stage returning to the initial state.
State how the net work and net change in internal energy are represented over a complete cycle on a P–V diagram.
[1]
Evaluate how the three stages could allow the device to operate as a heat engine, including the roles of heat input, heat rejection and irreversibility.
[1]
Question 49
A heat engine is being designed to operate between a high-temperature reservoir and a lake used as the cold reservoir.
Calculate the maximum efficiency if Th = 900 K and Tc = 300 K.
[1]
Discuss why this maximum efficiency cannot be exceeded and why a real high-power engine will be less efficient.
[1]
Question 50
A claim is made that, because local entropy can decrease in living organisms and in freezing water, the second law cannot apply to the universe as a whole.
Distinguish between isolated and non-isolated systems.
[1]
Evaluate the claim, referring to local entropy decrease, surroundings, irreversibility and the long-term evolution of the universe.
[1]
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