Thermodynamica 1. college 2 boek hoofdstuk 1. Bendiks Jan Boersma Wiebren de Jong Thijs Vlugt Theo Woudstra

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1 Thermodynamica Bendiks Jan Boersma Wiebren de Jong Thijs Vlugt Theo Woudstra Afdeling Process en Energie Sectie energietechniek February 4, 0 college boek hoofdstuk

2 summary lecture system (closed, open, adiabatic, isolated) state and properties intensive, extensive and specific properties process February 4, 0

3 systems: summary closed open general (diabatic) heat work heat matter work adiabatic work matter work isolated February 4, 0 3

4 systems: examples closed: refrigerator heat open: radiator heat mass work work mass adiabatic: coffee maker work isolated: cooler with hot bottle and freezer pack February 4, 0 4

5 process A process is defined as the change of the state of a system. We only consider changes from one equilibrium state to another The state of a system has changed when the properties (in an equilibrium state) have changed. During the change the system is not in equilibrium. A (thermodynamic) cycle is a process where the initial and final states are identical. adiabatic system adiabatic process isolated system isolated process February 4, 0 5

6 B process: examples A B A Reversible/irreversible? February 4, 0 6

7 Lecture February 4, 0 7

8 interpolation Properties of gases and liquids are given in tables (e.g., Table A-3). What is the boiling point at.3 bar? T? T T 0 Similar triangles: T p T p 0 0 T T p p 0 0 T T p 0 p p T 0 0 p p0 p p0 February 4, 0 8 T Answer: T = 06.7 C

9 What is the boiling point at.3 bar? T T T T 0 0 p p0 p p0 06.7C February 4, 0 9

10 thermal equilibrium A B A B heat conducting wall Two equilibrium systems that are brought into contact (via a heatconducting wall) will eventually reach a new equilibrium. This new equilibrium is such that both systems feel equally warm/cold : they are said to have the same temperature. How to quantify temperature? February 4, 0 0

11 0 th Law of Thermodynamics C C A B A B C C A B A B When C is in thermal equilibrium with A and B, then A and B are also in thermal equilibrium. This defines the experimental temperature for thermometer C February 4, 0 by measuring a property that uniquely depends on the temperature.

12 the experimental temperature Example: the property is the expansion of a fluid (mercury or alcohol). The centigrade scale is obtained at atmospheric pressure (.035 bar) by calling the freezing point 0 C and the boiling point 00 C. mercury thermometer boiling point of water alcohol thermometer We have a problem: what is the correct value? February 4, 0

13 the gas temperature scale (page 6-7) for the gas temperature scale we use a constant-volume gas thermometer The experimental gas temperature is defined as: T exp = p The constant is fixed for the water triple point (0.0 C) and refer to this value as 73.6 on the scale: where p tp is the triple point gas pressure exp February 4, 0 3 T p p tp

14 the gas temperature scale when the amount of gas is reduced we find for different gases: T exp 73.6 lim p tp 0 p p tp After consideration of the nd Law it will be shown that this scale is identical to the thermodynamic temperature scale when we use the triple point as a calibration point. February 4, 0 4

15 Temperatuur Bij thermo berekeningen moet je onzettend opletten met de temperatuur schaal, Kelvin of Celsius. Celsius werkt soms, Kelvin werkt altijd. Reken alle temperaturen altijd eerst om naar Kelvin!!! Wordt het antwoord gevraagd in Celsius reken dit dan pas helemaal op het eind om van Kelvin naar Celsius!!! February 4, 0 5

16 Potential energy Kinetic energy? February 4, 0 6

17 Kinetic, potential energy and heat PE KE Heat mgh mv mv mc p T PE.. Heat T Experiment with small lead (C 30 J / Kg K) or brass ( C 380 J / KgK) balls p gh C p p h 0 meters, T=? February 4, 0 7

18 mechanical energy trajectory d V Newton: F m dt V (bold) is velocity vector February 4, 0 8

19 We find that: F V m and so: dv dt V t t m d F V dt d V d mv V V dt mv m mv dt dt where: external work: kinetic energy (KE): t t F V dt mv s s F ds s s F s ds thus: external work KE KE KE February 4, 0 9

20 m R z z mg z F mge z R February 4, 0 0

21 External work: Substitute: where: thus: s s s s F ds R ds mgz mv mgz mv R ds February 4, 0 s s mgz potential energy of gravity (PE): mgz mgz External work of R = KE KE + PE PE = KE + PE When R = 0 : KE + PE = 0 or KE + PE = constant

22 work The work W is the work acted by the system on the surroundings W > 0 : work is done by the system W < 0 : work is done on the system t s W F V dt F ds sur sur t s In general, the work W depends on the trajectory: W W W W Work is not a property. Power (work per unit time): W F sur V February 4, 0

23 example Work exerted by a gas on a piston. Consider a quasi-static process. system boundary area A p, V W piston? W F ext W W dx dx padx V V pdv pdv Quasi-static P will be uniformly distributed February 4, 0 3

24 p W > 0 expansion p W < 0 compression V dv V V dv V p February 4, 0 4 V V

25 Water raket wedstrijd 5 maart, 0 Mekelpark (voor de faculteit) Plastic cola fles (0.5 liter) Rubber stop of kurk Fiets pomp Prijs: 00 Euro voor grootste afstand (mits > 50 meter) poging per deelnemer (team) February 4, 0 5

26 Question.8 Gas expands from 500kPa to 00kPa, the initial volume is 0.m^3. Sketch the process in a P-V diagram and determine the work. (You can assume P V = Const). pv pv C pv p 0.*500 / V V m p area A p, V C V 3 W pdv dv C dv C ln 50 0 *ln(5) 80.4KJ V V V let op C[ln(V ) ln( V )] is wiskundig gezien het zelfde maar fysisch gezien niet. We kunnen geen ln(.) nemen van een volume ivm dimensies dx system boundary W piston? February 4, 0 6

27 Question.8 (modified) Consider the expansion on the previous slide to be at T=500K and P V = C TC=00 Subsequently the same gas is compressed from to at a temperature of 300K calculate the work for both steps. pv CT C p V T Pa m K 3 I: / 00 / CT V W pdv dv CTln 00500*ln(5) 80.4kJ V V II : pv CT CT V 0. W pdv dv CTln 00*300*ln 48kJ V V 0.5 W W 0 systeem levert netto arbeid motor!! Verandering in temperatuur (toe of afvoer van warmte) geeft aanleiding tot netto arbeid! February 4, 0 7

28 Remark on work W pdv W pdv Alleen voor een gesloten systeem February 4, 0 8

29 instructions Ch. & Ch. up to. have been treated. Read this carefully before the next lecture. Make (some of) the exercises.-.0. Make one or more of the exercises.-.4 (work by a gas in a quasistatic equilibrium under compression or expansion) The next lecture will deal with the remainder of Ch. (except.4., this will be done later) and Ch. 3 up to 3. February 4, 0 9