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Date November 2016 Marks available 3 Reference code 16N.3.SL.TZ0.10
Level Standard level Paper Paper 3 Time zone Time zone 0
Command term Calculate Question number 10 Adapted from N/A

Question

An ideal nuclear power plant can be modelled as a heat engine that operates between a hot temperature of 612°C and a cold temperature of 349°C.

Calculate the Carnot efficiency of the nuclear power plant.

[2]
a.

Explain, with a reason, why a real nuclear power plant operating between the stated temperatures cannot reach the efficiency calculated in (a).

[2]
b.

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.

[3]
c.

Discuss the production of waste heat by the power plant with reference to the first law and the second law of thermodynamics.

[3]
d.

Markscheme

correct conversion to K «622 K cold, 885 K hot»

\({\eta _{{\rm{Carnot}}}} = 1 - \frac{{{T_{{\rm{cold}}}}}}{{{T_{{\rm{hot}}}}}} = 1 - \frac{{622}}{{885}} = 0.297\) or 29.7%

Award [1 max] if temperatures are not converted to K, giving result 0.430.

a.

the Carnot efficiency is the maximum possible

the Carnot cycle is theoretical/reversible/impossible/infinitely slow

energy losses to surroundings «friction, electrical losses, heat losses, sound energy»

OWTTE

b.

0.71 × 0.297 = 0.211

Allow solution utilizing wasted power «78.9%».

1.33/0.211 × 0.789 = 4.97 «GW»

4.97 GW × 3600 = 1.79 × 1013 «J»  

Award [2 max] if 71% used as the overall efficiency giving an answer of 1.96 × 1012 J.

Award [3] for bald correct answer.

Watch for ECF from (a).

c.

Law 1: net thermal energy flow is QINQOUT

QOUT refers to “waste heat”  

Law 1: QINQOUT = ∆Q=∆W as ∆U is zero

Law 2: does not forbid QOUT=0

Law 2: no power plant can cover 100% of QIN into work

Law 2: total entropy must increase so some Q must enter surroundings  

OWTTE

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
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