Thermodynamics2

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Ch. 5

Isentropic Efficiencies --allows you to relate ideal (reversible or isentropic) processes to actual processes using isentropic efficiencies --actual process is analyzed using actual inlet and outlet conditions --ideal process is analyzed with actual inlet conditions and outlet conditions are defined by the best possible process

eta_nozzle=actual KE increase/isentropic KE increase

eta_compressor/pump=isentropic work in/actual work in

\eta_turbine=actual work out/isentropic work out

Why would you EVER analyze a system as reversible since that is impossible? Because it is easier. Here is how....

Same things apply for open systems as closed systems for defining terms of the entropy equation.

Isentropic (constant entropy) if adiabatic and reversible

A process is polytropic (n=k=Cp0/Cv0), if ideal gas, adiabatic, and reversible.

Gibbs - a thermodynamic relationship

Gibbs is a relationship between five different thermodynamic properties and is valid for ALL systems, Tds =du+Pdv

Enthalpy, \Delta h = \Delta u + Pv

Enthalpy is a made up property that combines three other properties. It is used for convenience

EMEC 320 - Thermodynamics

Conservation of Mass

Open Systems (Control Volume Approach, Constant Volume)

Transient

Steady

Multiple inlets and exits

Sum(mi)=Sum(me)

One inlet/ one exit

mdoti=mdote

Closed Systems (Control Mass Approach, Constant Mass)

m1=m2 \Delta m = 0

Second Law of Thermodynamics

Cycles

Refrigerator

Coefficient of Performance Actual COP, beta_ref=QL/W Carnot (ideal) COP, beta_ref=TL/(TH-TL)

Heat Pump

Coefficient of Performance Actual COP, beta_hp=Qh/W Carnot (ideal) COP, beta_hp=Th/(Th-TL)

Heat Engine

Thermal Efficiencies Actual Efficiency, \eta_he=W/Qh Carnot (ideal) Efficiency, \eta_he=1-TL/Th

Entropy Equation Sum(mdote*se)-Sum(mdoti*si)=\int delta Qdot/T +Sgen

Emptying/Filling a Tank

Single Inlet/Single Exit, se-si=\int q/T + sgen

Entropy Generation, sgen

Irreversible, sgen is positive

Reversible, sgen=0

Heat Transfer, \int q/T Can only calculate if you know how T changes through the device or process.

Adiabatic, \int q/T=0

Isothermal, \int q/T = q/T

Entropy change, calculate the same way as closed systems

Entropy Equation, S2-S1 = \int delta Q/T + Sgen

Entropy Generation, Sgen

if irreversible, Sgen>0

Also if irreversible.... (S2-S1)=Q/Tsurr + Sgen (universe)

if reversible, Sgen=0

Heat transfer, \int delta Q/T

if isothermal, \int delta Q/T=Q/Tsystem

if adiabatic, \int delta Q/T=0

Entropy Change, s2-s1

Type of process

Process, s2-s1~=0

Cycle, s2-s1=0

Substance Types

solids and liquids (no phase change), s2-s1=C*ln(T2/T1)

ideal gas, (s2-s1)=Cp0*ln(T2/T1)-R*ln(P2/P1)

when phase changes, use tables

First Law of Thermodynamics

Closed Systems (Control Mass Approach, Constant Mass) This is how you analyze systems that have no mass leaving or entering the system. Examples: piston cylinders, balloons, closed tanks, rigid tanks.

Energy Equation /Delta E = Q - W

Work, W

Other (usually given or what you are finding)

Chemical

Electrical

Shaft

Boundary Work

When boundary is moving (volume changes through the process), W=\int P dV

Linear, P=mV+b

Polytropic, P=C/V^n

Isothermal (constant temperature) and ideal gas, P=mRT/V

Isobaric, constant pressure P=C

Heat, Q

Usually this is given or it is what you are finding

Types

Radiation

Convection

Conduction

Total Energy, \Delta E

Internal Energy, \Delta U

If Solid or Liquid (no phase change)

\Delta u=C*\Delta T

If multi phase (water, refrigerant, or ammonia)

Use tables

Superheated Vapor

PTsat u>ug v>vg s>sg

Saturated Vapor

P=Psat T=Tsat u=ug (ditto for v, s, & h)

Saturated Mixture

P=Psat T=Tsat u=uf+x*ufg (ditto for v, s, & h)

Saturated Liquid

P=Psat T=Tsat u=uf (ditto for v, s, & h)

Compressed Liquid

P>Psat T

If ideal Gas

\Delta u = C_v0*\Delta T

Kinetic Energy, \Delta KE

Potential Energy, \Delta PE

Open Systems (Control Volume Approach, Constant Volume) This is how you analyze systems that have mass flowing in or out. Examples: nozzles, diffusers, pumps, turbines, compressors, heat exchangers, mixing chambers, etc.

Energy Equation, DEcv/Dt=Qdot-Wdot+Sum_e(mdot*(h+ke+pe))-Sum_i(mdot*(h+ke+pe))

Transient Systems

Filling or Emptying a Tank

Steady Systems

Multiple Inlets/Exits

Mixing Chambers

Heat Exchanger

Single Inlet/Single Exit q+h_i+ke_i+pe_i=w+h_e+ke_e+pe_e

Pipes/Ducts

Heater/Cooler/Boiler

Pumps

Compressors/Fans

Turbines/Expanders

Throttling Devices/Valves

Nozzle/Diffuser