Lecture 44: Review Thermodynamics I

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1 ME 00 Thermodynamics I Lecture 44: Review Thermodynamics I Yong Li Shanghai Jiao Tong University Institute of Refrigeration and Cryogenics 800 Dong Chuan Road Shanghai, 0040, P. R. China liyo@sjtu.edu.cn Phone: ; Fax:

2 What is Thermodynamics? Science to study how one energy changes from one to another Thermodynamics = Therme(heat) + dynamis(force) Energy exists in several forms, e.g., potential, kinetic, chemical, thermal, electrical, nuclear among many others During interactions in nature, energy simply changes from one form to another; but the total energy remains constant.

3 Basic Principles First law of thermodynamics» A statement of conservation of energy principle» Energy is a thermodynamic property; quantifies energy Second law of thermodynamics» Energy has quality as well as quantity. Actual processes occur in direction of decreasing quality of energy» Establishes direction and possibility for process» Provides means for measuring the quality of energy» Determines theoretical limits regarding the performance of engineering devices.3

4 »»System Terms and Concepts Thermodynamic system, Closed system, Open (flow) system Surroundings, System boundary, Adiabatic (insulated), Rigid, Isolated»»Property Intensive, Extensive Specific properties»»state»»phases»»equilibrium, Thermodynamic equilibrium Mechanical Eq Thermal Eq Phase Eq.-----Chemical Eq.»»Process Isothermal, Isobaric, Isochoric, Quasi-Equilibrium Process.4

5 First law of Thermodynamics Open System.5

6 Important Equipments Nozzles, diffusers, Turbines compressors pumps Throttling valve Heat exchanger Turbines compressors pumps.6

7 Second Law of Thermodynamics Clausius (C) statement It is impossible for any system to operate in such a way that the sole result would be an energy transfer by heat from acooler to a hotter body. Kelvin Planck (K-P) statement It is impossible for any system to operate in a thermodynamic cycle and deliver a net amount of energy by work to its surroundings while receiving energy by heat transfer from a single thermal reservoir..» Analytical form of the K-P statement Irreversibility Heat transfer through a finite temperature difference Unrestrained expansion of a gas or liquid to a lower pressure Spontaneous chemical reaction. Reversible cycle» there are no irreversibilities within the system as it undergoes the cycle» heat transfers between the system and reservoirs occur reversibly. Two Carnot corollaries irrev rev rev = rev.7

8 Thermal Efficiency A reversible power cycle operating between two thermal reservoirs. Four internally reversible processes: two adiabatic processes alternated with two isothermal processes..8

9 Entropy Entropy is a property, it has fixed values at fixed states. S between two specified states is the same no matter what path, reversible or irreversible. The integral of dq/t gives S only if the integration is carried out along an internally reversible path between the two states..9

Entropy Balance Closed system entropy balance Other

principle» the entropy of an isolated system during a

10 Entropy Balance Closed system entropy balance Other forms of the entropy balance Increase of entropy principle» the entropy of an isolated system during a process always increases or, in the limiting case of a reversible process, remains constant. In other words, it never decreases.» Control volume entropy rate balance Steady state.0

p-v-t Surface Subcooled liquid=compressed liquid

::: the triple line of the threedimensional p v T

11 p-v-t Surface Subcooled liquid=compressed liquid Saturated Liquid Liquid Vapor Mixture Triple point ::: the triple line of the threedimensional p v T surface projects onto a Saturated Vapor Superheated Vapor point on the phase diagram. water, p cr ~ bar; T cr ~ 374.C water, triple point defined at 0.0 o C 0.63 kpa.

12 Concepts Incompressible Substance model Incompressible Substance model::: An idealization to simplify evaluations of liquids or solids, the v () is assumed to be constant and the u assumed to vary only with T. v =const 0.

13 u, h, c of Ideal Gases specific internal energy depends only on T specific enthalpy depends only on T Important relation.3

14 Entropy liquid vapor mixture Compressed liquid Ideal Gas Variable c v and c p c v and c p are constants liquids and solids modeled as incompressible. Saturated liquid to saturated vapor at constant T and p.4

15 Isentropic Processes of air (IG) Isentropic process for air modeled as ideal gas exp[ s o ( T )/ R] p r ( T ) relative pressure. reduced pressure. vr( T ) RT / pr( T ) relative volume..5

16 Isentropic Processes of air (IG) with constant c T v k constant T p (k ) / k constant k p v constant.6

17 Polytropic Processes on p v and T s Diagrams pv n c n 0 p c n p / v c n k pv k c s c n RT pv c T c n v c.7

Isentropic Efficiencies Isentropic Efficiencies :::

performance that would be achieved under idealized

18 Isentropic Efficiencies Isentropic Efficiencies ::: Comparison between the actual performance of a device and the performance that would be achieved under idealized circumstances for the same inlet state and the same exit pressure. Turbine isentropic turbine efficiency Actual turbine work Isentropic turbine work h h h h s h > h s η t < isentropic compressor efficiency.8

19 .9 Expressions for the Work Control Volumes One-inlet, one-exit steady-state flow Internally reversible e e e e e i i i i i cv cv cv gz V h m gz V h m W Q dt de rev int Tds m Q cv ) ( ) ( z z g V V h h m Q m W cv cv ) ( ) ( int z z g V V h h Tds m W rev cv vdp dh Tds vdp h h Tds ) ( int z z g V V vdp m W rev cv

20 Analyzing Rankine Cycle---I Turbine Condenser Pump Boiler Thermal efficiency of the power cycle Back work ratio.0

Reheat: High quality (or superheated vapor) existing the turbine

21 Superheat : Superheat and Reheat» Reason: Increase average temperature for heat addition at a given boiler pressure increase in performance Reheat: High quality (or superheated vapor) existing the turbine without large superheat For a given T H can increase T b without reducing quality.

22 Refrigeration Cycle COP= T subcooling T sc Evaporator: The heat transfer rate is referred to as the refrigeration capacity. ( kw).» Another unit for the refrigeration capacity is the ton of refrigeration, = kj/min. Compressor T cond T evap 4 3 s T H T L superheat: T sh Condenser Throttling process.

23 Air Standard Cycles Air standard cycles are idealized cycles based on the following approximations: A fixed amount of air modeled as an ideal gas (working fluid). The combustion process is replaced by a heat transfer from an external source. There are no exhaust and intake processes as in an actual engine. The cycle is completed by a constant-volume heat transfer process taking place while the piston is at the bottom dead center position. All processes are internally reversible. Cold air-standard analysis The specific heats are assumed constant at T a..3

24 Otto Cycle and Diesel Cycle Air Standard Cycle for CI Engines: r p p p p p x 3 pressure ratio r th k r k Then, c th r k k(r ) c V V V Define : r c "cutoff ratio" compression ratio r V V V MEP max min 3 BDC TDC Wnet net work for one cycle V V displacement volume Thus, for a given r :! th,diesel th,otto.4

Brayton Cycle Notes: -For cycles with regeneration: q in relatively constant q in = (h 3 -h x )+(h 3 -h x ) ~ h 3 -h xo w net increases (by 4-5-6-6 o ) Reheater increases th,r - For cycles without

25 Brayton Cycle Notes: -For cycles with regeneration: q in relatively constant q in = (h 3 -h x )+(h 3 -h x ) ~ h 3 -h xo w net increases (by o ) Reheater increases th,r - For cycles without regen.: q in increases by h 5 -h 4 and w net increases (by o ) Reheater reduces th,r actual heat transfer h h h h maximum heat transfer h h h h x For constant specific heats: T c p(t T ) T T th,r c T p(t3 T 4 ) T3 4 T 3 Also, assuming ideal gas and isentropic expansion and compression: k k k k 4 4 T p p T T3 p3 p T.5

Lecture 35: Vapor power systems, Rankine cycle

ME 00 Thermodynamics I Spring 015 Lecture 35: Vapor power systems, Rankine cycle Yong Li Shanghai Jiao Tong University Institute of Refrigeration and Cryogenics 800 Dong Chuan Road Shanghai, 0040, P. R.