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Date	November 2017	Marks available	2	Reference code	17N.3.SL.TZ0.8
Level	Standard level	Paper	Paper 3	Time zone	0 - no time zone
Command term	Sketch	Question number	8	Adapted from	N/A

Question

A monatomic ideal gas is confined to a cylinder with volume 2.0 x 10^–3 m³. The initial pressure of the gas is 100 kPa. The gas undergoes a three-step cycle. First, the gas pressure increases by a factor of five under constant volume. Then, the gas expands adiabatically to its initial pressure. Finally it is compressed at constant pressure to its initial volume.

Show that the volume of the gas at the end of the adiabatic expansion is approximately 5.3 x 10^–3 m³.

[2]

a.

Using the axes, sketch the three-step cycle.

[2]

b.

The initial temperature of the gas is 290 K. Calculate the temperature of the gas at the start of the adiabatic expansion.

[2]

c.

Using your sketched graph in (b), identify the feature that shows that net work is done by the gas in this three-step cycle.

[2]

d.

Markscheme

$500\,000 \times {\left( {2 \times {{10}^{ - 3}}} \right)^{\frac{5}{3}}} = 100\,000 \times {V^{\frac{5}{3}}}$

V = 5.3 x 10^–3 «m³»

Look carefully for correct use of pV^γ = constant

a.

correct vertical and horizontal lines

curve between B and C

Allow tolerance ±1 square for A, B and C

Allow ECF for MP2

Points do not need to be labelled for marking points to be awarded

b.

use of PV = nRT OR use of $\frac{P}{T}$ = constant

T = «5 x 290 =» 1450 «K»

c.

area enclosed

work is done by the gas during expansion

OR

work is done on the gas during compression

the area under the expansion is greater than the area under the compression

d.

Examiners report

[N/A]

a.

[N/A]

b.

[N/A]

c.

[N/A]

d.

Syllabus sections

Option B: Engineering physics » Option B: Engineering physics (Core topics) » B.2 – Thermodynamics

Show 52 related questions

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Explain, without any calculation, why the pressure after this change would belower if the process was isothermal.
16N.3.SL.TZ0.10c:
The nuclear power plant works at 71.0% of the Carnot efficiency. The power produced is 1.33 GW. Calculate how much waste thermal energy is released per hour.
17M.3.SL.TZ2.7a.i:
Justify why the thermal energy supplied during the expansion AB is 416 J.
17N.3.SL.TZ0.8c:
The initial temperature of the gas is 290 K. Calculate the temperature of the gas at the start of the adiabatic expansion.
17M.3.SL.TZ2.7a.iii:
Show that the thermal energy removed from the gas for the change BC is approximately 330 J.
18M.3.SL.TZ2.7d.i:
Sketch, on the pV diagram, the complete cycle of changes for the gas, labelling the changes clearly. The expansion shown in (a) and (b) is drawn for you.
16N.3.SL.TZ0.10a:
Calculate the Carnot efficiency of the nuclear power plant.
17N.3.SL.TZ0.10c:
The final image of the Moon is observed through the eyepiece. The focal length of the eyepiece is 5.0 cm. Calculate the magnification of the telescope.
18M.3.SL.TZ1.7a:
Show that the pressure at B is about 5 × 10⁵ Pa.
17M.3.SL.TZ1.6a:
State what is meant by an adiabatic process.
17M.3.SL.TZ1.6b:
Identify the two isothermal processes.
19M.3.SL.TZ2.10bi:
Calculate the change in internal energy of the gas for the process A→B.
18N.3.SL.TZ0.7c.ii:
State, without calculation, during which change (A → B, B → C or C → A) the entropy of the gas decreases.
18N.3.SL.TZ0.7c.i:
The work done by the gas from A → B is 288 J. Calculate the efficiency of the cycle.
18N.3.SL.TZ0.7a.ii:
Show that at C the temperature is 254 K.
18M.3.SL.TZ2.7a:
Show that the final volume of the gas is about 53 m³.
18N.3.SL.TZ0.7a.i:
Show that at C the pressure is 1.00 × 10⁶Pa.
18M.3.SL.TZ2.7c:
Determine the thermal energy which enters the gas during this expansion.
16N.3.SL.TZ0.10b:
Explain, with a reason, why a real nuclear power plant operating between the stated temperatures cannot reach the efficiency calculated in (a).
16N.3.SL.TZ0.10d: Discuss the production of waste heat by the power plant with reference to the first law and...
17M.3.SL.TZ1.6e:
State a reason why a Carnot cycle is of little use for a practical heat engine.
19N.3.SL.TZ0.6b(iii): state and explain whether the second law of thermodynamics is violated.
18M.3.SL.TZ1.7b.ii:
For the process BC, calculate, in J, the change in the internal energy of the gas.
19N.3.SL.TZ0.6b(i):
determine the thermal energy removed from the system.
18M.3.SL.TZ1.7b.i:
For the process BC, calculate, in J, the work done by the gas.
18M.3.SL.TZ1.7c.ii:
Determine, without any calculation, whether the net work done by the engine during one full cycle would increase or decrease.
18M.3.SL.TZ2.7d.ii:
Outline the change in entropy of the gas during the cooling at constant volume.
18N.3.SL.TZ0.7b:
Show that the thermal energy transferred from the gas during the change B → C is 238 J.
19N.3.SL.TZ0.6a(ii):
Calculate the ratio $\frac{V_{A}}{V_{C}}$ .
17M.3.SL.TZ1.6c.ii:
The volume at B is 2.30 × 10^–3 $\,$ m³. Determine the pressure at B.
17N.3.SL.TZ0.8d:
Using your sketched graph in (b), identify the feature that shows that net work is done by the gas in this three-step cycle.
18M.3.SL.TZ2.7e:
There are various equivalent versions of the second law of thermodynamics. Outline the benefit gained by having alternative forms of a law.
18M.3.SL.TZ1.7d:
Outline why an efficiency calculation is important for an engineer designing a heat engine.
18M.3.SL.TZ2.7b:
Calculate, in J, the work done by the gas during this expansion.
18M.3.SL.TZ1.7b.iii:
For the process BC, calculate, in J, the thermal energy transferred to the gas.
17M.3.SL.TZ2.7a.ii:
Show that the temperature of the gas at C is 386 K.
20N.3.SL.TZ0.9b(i):
Calculate the pressure following this process.
20N.3.SL.TZ0.9a(i):
Calculate the work done during the compression.
20N.3.SL.TZ0.9a(ii):
Calculate the work done during the increase in pressure.
20N.3.SL.TZ0.9b(ii): Outline how an approximate adiabatic change can be achieved.
17M.3.SL.TZ1.6d.ii:
The volume at C is 2.90 × 10^–3 $\,$ m³. Calculate the temperature at C.
17N.3.SL.TZ0.8a:
Show that the volume of the gas at the end of the adiabatic expansion is approximately 5.3 x 10^–3 m³.
19N.3.SL.TZ0.6b(ii):
explain why the entropy of the gas decreases.
17M.3.SL.TZ1.6d.i:
Show that ${P_B}V_B^{\frac{5}{3}} = nR{T_C}V_C^{\frac{2}{3}}$
19N.3.SL.TZ0.6a(i):
Show that the pressure at B is about 130 kPa.
19M.3.SL.TZ2.10bii: Calculate the temperature at A if the temperature at B is −40°C.
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17M.3.SL.TZ2.7a.iv:
Determine the efficiency of the heat engine.
17M.3.SL.TZ1.6c.i:
Determine the temperature of the gas at A.
17M.3.SL.TZ2.7b:
State and explain at which point in the cycle ABCA the entropy of the gas is the largest.
19M.3.SL.TZ2.10a:
Show that the work done on the gas for the isothermal process C→A is approximately 440 J.

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Option B: Engineering physics » Option B: Engineering physics (Core topics)

Option B: Engineering physics