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Question 18M.3.SL.TZ1.7

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Date May 2018 Marks available [Maximum mark: 10] Reference code 18M.3.SL.TZ1.7
Level SL Paper 3 Time zone TZ1
Command term Calculate, Determine, Explain, Outline, Show that Question number 7 Adapted from N/A
7.
[Maximum mark: 10]
18M.3.SL.TZ1.7

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.

(a)

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

[2]

Markscheme

« p 1 V 1 5 3 = p 2 V 2 5 3 »

1.1 × 10 5 × 5 5 3 = p 2 × 2 5 3

p2 «= 1.1 × 10 5 × 5 5 3 2.5 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]

(b.i)

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

[1]

Markscheme

«W = pΔV»

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

= 1.52 × 103 «J»

 

Award [0] if POT mistake.

[1 mark]

(b.ii)

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

[1]

Markscheme

ΔU = 3 2 pΔV =  3 2 5.07 × 105 × 3 × 10–3 = 2.28 × 10–3 «J»

 

Accept alternative solution via Tc.

[1 mark]

(b.iii)

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

[1]

Markscheme

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

 

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

[1 mark]

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 × 10–3 m3.

(c.i)

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

[2]

Markscheme

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

since VC > VB, PC must be smaller than PB

[2 marks]

(c.ii)

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

[2]

Markscheme

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]

(d)

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

[1]

Markscheme

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

 

Allow any sensible answer.

[1 mark]

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