Thermodynamics :

first law

open system

closed system

second law

open system

closed system

Energy Equation,
DEcv/Dt=Qdot­Wdot+Sum_e(mdot
(h+ke+pe))­Sum_i(mdot(h+ke+pe)

transient system

steady system

multiple inlet/ exit

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

Nozzle/Diffuser Throttling Devices/Valves Turbines/Expanders
Compressors/Fans Pumps Heater/Cooler/Boiler
Pipes/Ducts

Energy Equation
/Delta E = Q ­ W

heat

conduction

convection

radiation

work

Boundary Work

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

Isobaric, constant pressure
P=C

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

Linear,
P=mV+b

Polytropic,
P=C/V^n

other

electrical

shaft

chemical

TOTAL ENERGY/delta e

potential energy

kinetic energy

internal energy

If ideal Gas
\Delta u = C_v0*\Delta T

If multi phase (water, refrigerant, or ammonia)

If Solid or Liquid (no phase change) \Delta u=C*\Delta T

use table

Compressed Liquid

Saturated Liquid

Saturated Mixture

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

P>Psat
T<Tsat
u<uf
v<vf
s<sf
If no compressed liquid table:
u~uf(at T)
(ditto for v, s, & h)

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

Saturated Vapor

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

Superheated Vapor

P<Psat T>Tsat
u>ug
v>vg
s>sg

Entropy Equation,
S2­S1 = \int delta Q/T + Sgen

Entropy Change, s2­s1

Type of process

Cycle, s2­s1=0

Process, s2­s1~=0

Substance Types

when phase changes,
use tables

ideal gas,
(s2­s1)=Cp0ln(T2/T1)­Rln(P2/P1)

solids and liquids (no phase change),
s2­s1=C*ln(T2/T1)

Heat transfer, \int delta Q/T

if adiabatic,
\int delta Q/T=0

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

Entropy Generation, Sgen

if reversible,
Sgen=0

if irreversible,
Sgen>0

Also if irreversible....
(S2­S1)=Q/Tsurr + Sgen (universe)

Entropy Equation
Sum(mdotese)­Sum(mdotisi)=\int delta
Qdot/T +Sgen

Steady Systems

Multiple Inlets/Exits

Single Inlet/Single Exit,
se­si=\int q/T + sgen

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

Isothermal,
\int q/T = q/T

Adiabatic,
\int q/T=0

Entropy change,
calculate the same way as closed systems

transient system

cycles

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

Heat Pump
Coefficient of Performance
Actual COP,
beta_hp=Qh/W
Carnot (ideal) COP,
beta_hp=Th/(Th­TL)

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

Conservation of Mass

Closed Systems
(Control Mass Approach, Constant Mass)
m1=m2
\Delta m = 0

Open Systems
(Control Volume Approach, Constant Volume)

Steady

One inlet/ one exit
mdoti=mdote
M

Multiple inlets and exits
Sum(mi)=Sum(me)

Transient