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Date	November 2018	Marks available	2	Reference code	18N.3.SL.TZ0.7
Level	Standard level	Paper	Paper 3	Time zone	0 - no time zone
Command term	Show that	Question number	7	Adapted from	N/A

Question

The pV diagram of a heat engine using an ideal gas consists of an isothermal expansion A → B, an isobaric compression B → C and an adiabatic compression C → A.

The following data are available:

Temperature at A = 385 K

Pressure at A = 2.80 × 10⁶Pa

Volume at A = 1.00 × 10^–4m³

Volume at B = 2.80 × 10^–4m³

Volume at C = 1.85 × 10^–4m³

Show that at C the pressure is 1.00 × 10⁶Pa.

[2]

a.i.

Show that at C the temperature is 254 K.

[2]

a.ii.

Show that the thermal energy transferred from the gas during the change B → C is 238 J.

[3]

The work done by the gas from A → B is 288 J. Calculate the efficiency of the cycle.

[2]

c.i.

State, without calculation, during which change (A → B, B → C or C → A) the entropy of the gas decreases.

[1]

c.ii.

Markscheme

ALTERNATIVE 1:

${P_c} = {P_B} = \frac{{{P_A}{V_A}}}{{{V_B}}}$ ✔

= $\frac{{2.8 \times {{10}^6} \times 1 \times {{10}^{ - 4}}}}{{2.8 \times {{10}^{ - 4}}}}$ «= 1.00 × 10⁶Pa» ✔

ALTERNATIVE 2:

$2.8 \times {10^6} \times {1.00^{\frac{5}{3}}} = {P_c} \times {1.85^{\frac{5}{3}}}$ ✔

${P_c} = 2.8 \times {10^6} \times \frac{{{{1.00}^{\frac{5}{3}}}}}{{{{1.85}^{\frac{5}{3}}}}}$ «= 1.00 × 10⁶Pa» ✔

a.i.

ALTERNATIVE 1:

Since T_B = T_A then T_c = $\frac{{{V_c}{T_B}}}{{{V_B}}}$ ✔

= $\frac{{1.85 \times 385}}{{2.8}}$ «= 254.4K» ✔

ALTERNATIVE 2:

$\frac{{2.80 \times 1.00}}{{385}} = \frac{{1.00 \times 1.85}}{{{T_c}}}$ «K»✔

${T_c} = 385 \times \frac{{1.00 \times 1.85}}{{2.80}}$ «= 254.4K» ✔

a.ii.

work done = «pΔV = 1.00 × 10⁶ × (1.85 × 10⁻⁴ − 2.80 × 10⁻⁴ =» −95 «J» ✔

change in internal energy = « $\frac{3}{2}$ pΔV = − $\frac{3}{2}$ × 95 =» −142.5 «J» ✔

Q = −95 − 142.5 ✔

«−238 J»

Allow positive values.

net work is 288 −238 = 50 «J» ✔

efficiency = « $\frac{{288 - 238}}{{288}}$ =» 0.17 ✔

c.i.

along B→C ✔

c.ii.

Examiners report

[N/A]

a.i.

[N/A]

a.ii.

[N/A]

c.i.

[N/A]

c.ii.

Syllabus sections

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

Show 52 related questions

17N.3.SL.TZ0.8b: Using the axes, sketch the three-step cycle.
18M.3.SL.TZ1.7c.i:
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.
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.
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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

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