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Date May 2019 Marks available 2 Reference code 19M.3.SL.TZ2.10
Level Standard level Paper Paper 3 Time zone 2
Command term Suggest Question number 10 Adapted from N/A

Question

A heat pump is modelled by the cycle A→B→C→A.

The heat pump transfers thermal energy to the interior of a building during processes C→A and A→B and absorbs thermal energy from the environment during process B→C. The working substance is an ideal gas.

Show that the work done on the gas for the isothermal process C→A is approximately 440 J.

[2]
a.

Calculate the change in internal energy of the gas for the process A→B.

[2]
bi.

Calculate the temperature at A if the temperature at B is 40°C.

[1]
bii.

Determine, using the first law of thermodynamics, the total thermal energy transferred to the building during the processes C→A and A→B.

[3]
c.

Suggest why this cycle is not a suitable model for a working heat pump.

[2]
d.

Markscheme

evidence of work done equals area between AC and the Volume axis ✓

reasonable method to estimate area giving a value 425 to 450 J ✓

Answer 440 J is given, check for valid working.

Examples of acceptable methods for MP2:

- estimates 17 to18 small squares x 25 J per square = 425 to 450 J.
- 250 J for area below BC plus a triangle of dimensions 5 × 3, 3 × 5, or 4 × 4 small square edges giving 250 J + 187.5 J or 250 J + 200 J.

Accurate integration value is 438 J - if method seen award [2].

a.

«use of  U = 3 2 n R T and  p V = n R T to give»

Δ U = 3 2 Δ p V  ✔

« = 3 2 × 2.5 × 10 5 × 1 × 10 3 »

=«–»375«J»  ✔

Another method is possible: eg realisation that ΔU for BC has same magnitude, so ΔU = 3/2 PΔV.

bi.

TA = 816«K» OR  543«°C»

bii.

for CA ΔU = 0 so Q = W = −440 «J» ✔

for AB W = 0 so Q = ΔU = 375 «J» ✔

815 «J» transferred to the building ✔

Must use the first law of thermodynamics for MP1 and MP2.

c.

the temperature changes in the cycle are too large ✔

the cycle takes too long «because it contains an isothermal stage» ✔

energy/power output would be too small ✔

d.

Examiners report

At SL, Correct answers were rare and very few candidates used the fact the work done was area under the curve, and even fewer could estimate this area. At HL, the question was better answered. Candidates used a range of methods to estimate the area including counting the squares, approximating the area using geometrical shapes and on a few occasions using integral calculus.

a.

Not very many candidates seem to know the generalised formula ΔU =1.5(P2V2 -P1V1) however many correct answers were seen.

bi.

The temperature at A was found correctly by most candidates.

bii.

The main problem here was deciding whether each Q was positive or negative. But the question was quite well answered.

c.

Because the question was about a heat pump rather than a heat engine very few answers were correct. Only a very small number of candidates mentioned the fact that the isothermal change would take an impracticably long time.

d.

Syllabus sections

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