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compressible exam 1: review
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Gravity
Terms in this set (30)
open system
exchange of mass and energy
closed system
exchange of energy, first law only for closed systems
isolated system
no exchange, dw=0
P units
Pa [kg/m/s^2], N/m^2 (N=kg*m/s^2)
R units
J/kg/K (J=kg*m^2/s^2)
T units
K=C+273
s units
J/K (J=kg*m^2/s^2)
h units
J/kg (J=kg*m^2/s^2)
ideal gas
-large number of molecules
-volume of molecules << volume of gas
-only forces are elastic collisions (dE=0)
thermodynamic processes on PV diagram
-reversible: closed loop
-irreversible: not a closed loop
-adiabatic: linear, negative slope
-isothermal: curved line going down (PV constant for constant T)
-isobaric: horizontal line
-isentropic: curved line going down (PV^γ=c)
-isochoric: vertical line
thermodynamic processes on TS diagram
-adiabatic: vertical line (adiabatic + reversible = isentropic)
-isothermal: horizontal line
-isobaric: curved line going up
-isentropic: vertical line
-isochoric: linear, positive slope
-reversible: vertical line
-irriversible: increasing s
first law of thermodynamics
∆U=∆Q-∆W for a closed system
internal energy
sum of the kinetic and potential energies of the atoms and molecules of the system
enthalpy
heat content, h=u+pv=u+p/ρ
how to change h₀
∆Q or ∆W
second law of thermodynamics
an irreversible process will increase entropy and a reversible process will have constant entropy unless work is done (ds=dq/T+ds_irreversible)
specific heats definitions
constant pressure: ∆h=cp∆T
constant volume: ∆u=cv∆T
calorically perfect
cp and cv are constant, h₀=cpT₀
wave motion
-transverse: wave is perpendicular to motion
-longitudinal: wave is parallel to motion
sound
-longitudinal wave, variation of velocity and pressure
-small sound disturbances are treated as isentropic (reversible and adiabatic)
speed of sound
speed at which small (reversible) disturbances travel into a quiescent (at rest) fluid, depends on compressibility
stagnation pressure
pressure where v=0
during a stagnation process:
kinetic energy is converted to enthalpy
stagnation enthalpy
-enthalpy of a fluid when it's brought to rest reversibly and adiabatically
-remains constant for steady, adiabatic flow when energy is conserved
-h₀=h+v²/2
-ideal gas: h=cpT
shock
-abrupt change in fluid properties in a very small region of space
-always compressive (P↑, v↓)
there will be a shock if
Pexit<Pambient
mach cone
-M<1: all fluid elements around the source receive information about it
-M=1: v=a, source and disturbance move together, there is a line and stuff on the other side doesn't know about the shock
-M>1: Mach cone, sinμ=1/M
characteristic mach number
-at M=1, characteristic thermodynamic properties are defined
-M*=v/a*
-M*²=[(γ+1)M²]/[2+(γ-1)M²]
property changes across shock
•M1>1, M2<1
•V2<V1
•P2>P1
•ρ2>ρ1
•T2>T1
•s2>s1
•P02<P01
•h02=h01
•T02=T01
increase in entropy across shock causes
stagnation pressure loss
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