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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

Eksaminatore / Examiners: Dr. J. Dirker, Dr. L. Martins

Semestertoets 2 Tyd: 90 minute September 2014 Maksimum Punte: 50

Instruksies • Beantwoord alle vrae. • Tabelle en ʼn formuleblad word verskaf. • Begin elke vraag op ʼn nuwe bladsy. • Netheid vergemaklik dit om punte te identifiseer. • Maak asb. gebruik van diagramme en definieer

enige punte of veranderlike van belang, daarop.

Semester Test 2 Time: 90 minutes September 2014 Maximum Marks: 50

Instructions • 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

point or variable of interest on it.

Vraag 1 [10 Punte]

ʼn Ideale gas (R = 150 J/kgK) ondergaan ʼn verhitting-proses waartydens die temperatuur styg met 20°C, die druk verdubbel, en die volume toeneem met 15%. Deur die hitte-oordrag en arbeid verrig te meet tydens die proses, is dit bekend dat die spesifieke interne energie toeneem met 9823 J/kg. Bereken die volgende: 1.1 Die gemiddelde CV,0 [J/kgK] waarde. (2) 1.2 Die spesifieke entalpie toename [J/kg]. (3)1.3 Die spesifieke entropie toename [J/kgK] (5)

Question 1 [10 Marks]

An ideal gas (R = 150 J/kgK) goes through a heating process during which its temperature increases by 20°C, its pressure doubles, and volume increases by 15%. By measuring the heat transfer and work done during the process, it is know that the specific internal energy increased by 9823 J/kg. Calculate the following: 1.1 The average CV,0 [J/kgK] value. (2) 1.2 The specific enthalpy increase [J/kg]. (3)1.3 The specific entropy increase [J/kgK] (5)

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Vraag 2 [24 Punte]

Beskou ʼn pneumatiese hyser getoon in die figuur wat bedryf word met ideale lug. Die hyser moet ʼn massa van mp = 10 kg oplig en die atmosfeer verplaas d.m.v. ʼn wrywinglose suier-silinder met ʼn binne-diameter van D = 100 mm. Lug word in die suier gedwing via ʼn kompressor wat lug intrek teen ʼn gestadigde tempo van m = 0.003 kg/s vanaf die atmosfeer teen PA = 100 kPa en TA = 300 K. Die kompressor verbruik drywing teen ʼn gestadigde tempo van 520 W en verloor hitte teen ʼn gestadigde tempo van 350 W. Aanvaar alle snelhede is laag. Waar van toepassing gebruik Tabel A.7.1 en bereken die volgende vir punt B (by die uitlaat van die kompressor): 2.1 Druk PB [Pa] (Wenk: hierdie is ook die druk

binne die silinder). (4) 2.2 Temperatuur TB [K] (Kies u eie kontrole-

oppervlak). (6) Beskou nou die volume binne die suier/silinder en wat daarmee gebeur vanaf toestand 1 tot toestand 2 terwyl die kompressor die silinder vul met lug oor ʼn tydsduur van Δt = 11 sekondes en die suier opbeweeg. By toestand 1 is die volgende bekend: y1 = 0.2 m en T1 = 320 K, en by toestand 2 is die temperatuur T2 = 340 K.

Question 2 [24 Marks]

Consider a pneumatic lift shown in the figure, operated with ideal air. The lift should raise a mass of mp = 10 kg and displace the atmosphere by using a frictionless piston-cylinder, which has an inner diameter of D = 100 mm. Air is forced into the piston by means of a compressor which draws in air at a steady rate of m = 0.003 kg/s from the atmosphere at PA = 100 kPa and TA = 300 K. The compressor consumes power at a steady rate of 520 W and has a heat loss at a steady rate of 350 W. Assume all velocities to be low. Where applicable, use table A.7.1 and calculate the following for point B (at the exit of the compressor): 2.1 Pressure PB [Pa] (Hint: this is also the

pressure in the cylinder). (4) 2.2 Temperature TB [K] (Select your own control

surface). (6)

Now consider the volume inside the piston/cylinder and what happens to it from state 1 to state 2 as the compressor fills the cylinder with air over a time period of Δt = 11 seconds and the piston moves up. At state 1 the following is known: y1 = 0.2 m and T1 = 320 K, and at state 2 the temperature is T2 = 340 K.

y1

y21

2

D

mp

AB

Compressor / Kompressor

AIR / LUG

CV

g= 9.81 m/s2

Figuur: Pneumatiese hyser aangedryf deur ʼn kompressor. Figure: Pneumatic lift driven by a compressor.

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Vraag 2 (vervolg)

Waar van toepassing, gebruik Tabel A.7.1 en bereken die volgende (gebruik die kontrole oppervlak soos aangedui in die figuur): 2.3 Die massa lug wat die silinder invloei, mi [kg]

(2)2.4 Die arbeid verrig deur die volume, WCV [J]. (7) 2.5 Die hitte-verlies vanaf die lug binne die

silinder, QCV [J]. (5)

Question 2 (continued)

Where applicable, use Table A.7.1 and calculate the following (use the control surface as is shown in the figure): 2.3 The mass of air that flowed into the cylinder,

mi [kg]. (2)2.4 The work done by the volume, WCV [J]. (7)2.5 The heat lost by the air inside the cylinder,

QCV [J]. (5)

Vraag 3 [16 Punte]

Beskou ʼn starre houer wat ms = 1200 kg gesmelte Litium-nitried sout (vloeistof) bevat wat per dag via gekonsentreerde son-energie verhit word. Terwyl dit ʼn vloeistof is, het die sout ʼn konstante spesifieke hitte van 935 J/kgK.

Die gestoorde energie word snags gebruik om ʼn hitte-enjin aan te dryf wat ʼn termiese rendement het van 50% van die termiese rendement van ʼn Carnot hitte-enjin. Die nag-proses begin by ʼn sout-temperatuur van TH1 = 820 K en stop teen TH2 = 570 K. Die hitte-enjin word verkoel deur ʼn groot water-liggaam waarvan die temperatuur konstant bly teen TL = 290 K (weens die brute grootte daarvan).

3.1 Bereken die termiese rendement van die hitte-enjin aan die begin van die proses. (2)

SLAAN-OOR NA 3.3 INDIEN U NIE DIE VOLGENDE VRAAG KAN DOEN NIE: 3.2 Bereken die totale arbeid [J] wat die hitte-

enjin produseer per nag. Begin u berekening met die oombliklike rendement van die hitte-enjin:

η = δW/ δQH

(Let wel dat die rendement ʼn funksie is van die sout-temperatuur). (6)

ʼn Verstelling was aan die hitte-enjin gemaak om die rendement te verhoog. Daar word nou beweer dat dit ws = 110 kJ/kg totale arbeid per kg sout tydens die nag-proses produseer. Bereken die volgende vir die nag-proses:

3.3 Entropie-verandering [J/K] van die sout. (2) 3.4 Entropie-verandering [J/K] van die water -

liggaam. (4) 3.5 Totale entropie-generasie [J/K] (2)

Question 3 [16 Punte]

Consider a rigid vessel containing ms = 1200 kg of molten Lithium-nitride salt (liquid) which was heated during the day via concentrated solar energy. While in liquid phase, the salt has a constant specific heat of 935 J/kgK.

The stored energy is used during the night to drive a heat engine which has a thermal efficiency that is 50% of the thermal efficiency of a Carnot heat engine. The night process starts at a salt temperature of TH1 = 820 K and is stopped at TH2 = 570 K. The heat engine is cooled by a large water body whose temperature remains constant at TL = 290 K (due to its sheer size).

3.1 Calculate the thermal efficiency of the heat engine at the start of the process. (2)

SKIP TO 3.3 IF YOU ARE NOT ABLE TO DO THE FOLLOWING QUESTION: 3.2 Calculate the total amount of work [J] that the

heat engine produces per night. Start your calculation with the instantaneous efficiency of the heat engine:

η = δW/ δQH

(Note that the efficiency is a function of the salt temperature). (6)

An adjustment was made to the heat engine to increase its efficiency. It is now claimed that it produces ws = 110 kJ/kg of total work per kg of salt during the night process. Calculate the following for the night process:

3.3. Entropy change [J/K] of the salt. (2)3.4 Entropy change [J/K] of the water body. (4)

3.5 Total entropy-generation [J/K]. (2)

FORMULEBLAD VOLG / FORMULAE SHEET FOLLOWS

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