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Date	May 2018	Marks available	1	Reference code	18M.3.SL.TZ1.7
Level	Standard level	Paper	Paper 3	Time zone	1
Command term	Calculate	Question number	7	Adapted from	N/A

Question

The pressure–volume (pV) diagram shows a cycle ABCA of a heat engine. The working substance of the engine is 0.221 mol of ideal monatomic gas.

At A the temperature of the gas is 295 K and the pressure of the gas is 1.10 × 10⁵ Pa. The process from A to B is adiabatic.

The process from B to C is replaced by an isothermal process in which the initial state is the same and the final volume is 5.00 × 10^–3m³.

Show that the pressure at B is about 5 × 10⁵ Pa.

[2]

For the process BC, calculate, in J, the work done by the gas.

[1]

b.i.

For the process BC, calculate, in J, the change in the internal energy of the gas.

[1]

b.ii.

For the process BC, calculate, in J, the thermal energy transferred to the gas.

[1]

b.iii.

Explain, without any calculation, why the pressure after this change would belower if the process was isothermal.

[2]

c.i.

Determine, without any calculation, whether the net work done by the engine during one full cycle would increase or decrease.

[2]

c.ii.

Outline why an efficiency calculation is important for an engineer designing a heat engine.

[1]

Markscheme

« ${p_1}V_1^{\frac{5}{3}} = {p_2}V_2^{\frac{5}{3}}$ »

$1.1 \times {10^5} \times {5^{\frac{5}{3}}} = {p_2} \times {2^{\frac{5}{3}}}$

p₂ «= $\frac{{1.1 \times {{10}^5} \times {5^{\frac{5}{3}}}}}{{{{2.5}^{\frac{5}{3}}}}}$ » = 5.066 × 10⁵ «Pa»

Volume may be in litres or m³.

Value to at least 2 sig figs, OR clear working with substitution required for mark.

[2 marks]

«W = pΔV»

«= 5.07 × 10⁵ × (5 × 10^–3 – 2 × 10^–3)»

= 1.52 × 10³ «J»

Award [0] if POT mistake.

[1 mark]

b.i.

ΔU = $\frac{3}{2}$ pΔV = $\frac{3}{2}$ 5.07 × 10⁵ × 3 × 10^–3 = 2.28 × 10^–3 «J»

Accept alternative solution via T_c.

[1 mark]

b.ii.

Q «= (1.5 + 2.28) × 10³ =» 3.80 × 10³ «J»

Watch for ECF from (b)(i) and (b)(ii).

[1 mark]

b.iii.

for isothermal process, PV = constant / ideal gas laws mentioned

since V_C > V_B, P_C must be smaller than P_B

[2 marks]

c.i.

the area enclosed in the graph would be smaller

so the net work done would decrease

Award MP2 only if MP1 is awarded.

[2 marks]

c.ii.

to reduce energy loss; increase engine performance; improve mpg etc

Allow any sensible answer.

[1 mark]

Examiners report

[N/A]

b.i.

[N/A]

b.ii.

[N/A]

b.iii.

[N/A]

c.i.

[N/A]

c.ii.

[N/A]

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.
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.
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.
19M.3.SL.TZ2.10c: Determine, using the first law of thermodynamics, the total thermal energy transferred to the...
19M.3.SL.TZ2.10d: Suggest why this cycle is not a suitable model for a working heat pump.
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)

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