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UNIVERSITEIT VAN PRETORIA UNIVERSITY OF PRETORIA

Departement Meganiese en Lugvaartkundige Ingenieurswese Department of Mechanical and Aeronautical Engineering

Termodinamika MTX221 Thermodynamics MTX221

Eksaminator / Examiner: Dr. J. Dirker

Semestertoets 2 Tyd: 90 minute Oktober 2009 Punte: 50 Instruksies • LET ASB: Hierdie Vraestel is uit 50 punte. • Beantwoord alle vrae. • Tabelle en ‘n formuleblad word verskaf. • Begin elke vraag op ‘n nuwe bladsy. • Netheid maak dit makliker om punte te sien. • Maak asb. gebruik van diagramme en definieer enige punte van belang met ‘n gepaste nommer.

Semester Test 2 Time: 90 minutes October 2009 Marks: 50

Instructions

• PLEASE NOTE: This paper is out of 50 marks. • Answer all questions. • Tables and a formula sheet are supplied. • Start every question on a new page. • Neatness makes it easier to identify marks. • Please make use of diagrams and define any points of interest with a suitable number.

VRAAG 1 [17] ‘n Stoomkragstasie word intern op ‘n Carnot kringloop bedryf. Hitte word onderskeidelik by konstante interne temperature ontvang en verwerp. Die volgende inligting aangaande die kringloop is beskikbaar: Beskrywing T x h ºC kJ/kg 1 Turbine inlaat 350 2 Kondensator inlaat 1.0 3 Pomp inlaat 80 1275.7 4 Verdamper inlaat 350 0.0

a) Gebruik die bo-staande nommers en maak ‘n

skematiese voorstelling van die kragstasie. Sluit die volgende in: hoofkomponente, termiese reservoirs, vloeirigting, asook hitte en arbied oordragte (9)

b) Indien die turbine (1 →2) ‘n inlaat snelheid

van 50 m/s het, bepaal die spesifieke arbeid uitset van die turbine [kJ/kg] (aanvaar die uitlaat spoed is weglaatbaar klein). (8)

QUESTION 1 [17] A steam power plant is operated internally on a Carnot cycle. Heat is received end rejected at constant internal temperatures respectively. The following information is available regarding the cycle: Description T x h ºC kJ/kg 1 Turbine inlet 350 2 Condenser inlet 1.0 3 Pump inlet 80 1275.7 4 Evaporator inlet 350 0.0

a) Use the above-given numbers and make a schematic representation of the power plant. Include the following: main components, thermal reservoirs, flow direction, as well as heat and work transfers. (9)

b) If the turbine (1 →2) has an inlet velocity of

50 m/s, calculate the specific work output of the turbine [kJ/kg] (assume the exit velocity is negligibly small). (8)

Kopiereg voorbehou Copyright reserved

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VRAAG 2 [24] Beskou die onderstaande silinder /suier wat aan die bokant 3 kg lug bevat en aan die onderkant ‘n onbekende hoeveelheid ammoniak. Aanvanklik is die lug en ammoniak beide teen 30ºC en 100 kPa. Die suier se massa kan geïgnoreer word. Die onderste volume word d.m.v ‘n klep aan ‘n ammoniak lyn teen 1600 kPa en 340 ºC verbind. Die klep word oopgemaak en bykomende ammoniak vloei in die onderste gedeelte in sodat die suier boontoe beweeg. Gedurende hierdie proses word die lug politropies saam-gedruk met ‘n politropiese eksponent van 1.6. Wanneer die klep gesluit word is beide die lug en ammoniak teen 800 kPa en 300 ºC. a) Bereken die arbeid wat op die lug verrig word. (4) b) Wat is die lug se entropie toename? (4) c) Indien die ammoniak aanvanklik ‘n volume van

0.1 m3 gahad het, bereken die hitte-oordrag na/van die ammoniak tydens hierdie proses

(Wenk: gebruik die lug se volume-verandering om die ammoniak se finale volume te verkry)

(16)

QUESTION 2 [24]

Consider the cylinder/ piston shown below containing 3 kg air above the piston and an unknown amount of ammonia below the piston. Initially the air and ammonia are both at 30ºC and 100 kPa. The mass of the piston may be ignored. The volume below the piston is connected via a valve with an ammonia line at 1600 kPa and 340ºC. The valve is opened and additional ammonia flows into the bottom volume such that the piston moves upward. During this process the air is compressed in a polytropic process with a polytropic exponent of 1.6. When the valve is closed, both the air and the ammonia are at 800 kPa and 300ºC.

a) Calculate the work done on the air. (4) b) What is the increase in entropy of the air?

(4) c) If the ammonia had an initial volume of

0.1 m3, determine the heat transfer to/ from the ammonia during this process.

(Hint: use the volume change of the air to determine the final volume of the ammonia) (16)

1

Air / Lug

Ammonia / Ammoniak

2 Politropic / Politropies

Air / Lug

Ammonia / Ammoniak

Figuur / Figure

(Vraag 2 / Question 2)

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VRAAG 3 [9] ‘n Hitte pomp het ‘n werksverrigtingskoëffisiënt (COP) van 50% van die teoretiese maksimum. Dit word gebruik om ’n huis in die winter te verhit sodat ’n binne temperatuur van 20°C onderhou word. Die huis lek hitte na die koue omgewing teen ‘n tempo van 400 W per graad temperatuur verskil met die omgewing:

( )LHlek TTQ −= 400& [W] a) Vir die geval waar slegs 1 kW beskikbaar is om

die hittepromp aan te dryf, bereken die mini-mum buite temperatuur waarvoor die hitte-pomp genoegsame verhitting sal verskaf. (5)

In die somer kan dieselfde opstelling gebruik word as ‘n lugreelaar om die huis af te koel (deur die kompressor se inlaat en uitlaat poorte d.m.v. klep verstellings om te ruil). Na inspeksie van die huis, die stelsel, en verrigtings-data, is ‘n konsultant van mening dat ‘n werksverrigtings-koëffisiënt (COP) van 10 toepaslik is tydens verkoeling. b) Deur gepaste berekeninge te maak bepaal of

sy/haar stelling geldig is. (4)

QUESTION 3 [9] A heat pump has a coefficient of performance (COP) of 50% of that of the theoretical maximum. It is used to heat a house in the winter such that an internal temperature of 20ºC is maintained. The house leaks heat to the colder environment at a rate of 400 W per degree temperature difference with environment:

( )LHleak TTQ −= 400& [W] a) In the case where only 1 kW is available to

drive the heat pump, calculate the minimum outside temperature for which the heat pump will be able to supply sufficient heating. (5)

During summer the same set-up could be used as an air-conditioner to cool the house (by swapping the compressor’s inlet and outlet port via a valve adjustment). After inspecting the house, the system, and the performance data, a consultant is of opinion that a coefficient of performance (COP) of 10 is applicable during cooling. b) By making appropriate calculations, deter-

mine if his/ her statement is valid. (4)

Formuleblad volg…. Formulae Sheet follows….

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Formule Blad / Formulae Sheet

fgf xφφφ +=

ZRTPv = PVUH +=

PdVW =δ .constPV n =

v

v TuC ⎟⎠⎞

⎜⎝⎛∂∂

= p

p ThC ⎟⎠⎞

⎜⎝⎛∂∂

=

HQ

W=η

WQ HL /=β

PdVdUTdS += VdPdHTdS −=

mgZmVUE ++=2

2

∑ ∑ =−= 0ie mmdtdm

&&

∫ ∫= WQ δδ

212

22

21

21

121 22WmgZmVUmgZmVUQ +++=+++

∑ ∑ ++++=+++ WgZV

hmdtdEgZ

VhmQ e

eeei

iii

&&&& )2

()2

(22

0≤∫ TQδ

genSTQdS δδ+=

∑ ∑ ∑ +=−+ geniiee STQsmsm

dtdS &

&&&

kk

PP

TT

1

1

2

1

2

−

⎟⎟⎠

⎞⎜⎜⎝

⎛=

1

2

1

1

2

−

⎟⎟⎠

⎞⎜⎜⎝

⎛=

k

VV

TT

k

VV

PP

⎟⎟⎠

⎞⎜⎜⎝

⎛=

2

1

1

2