Q&A_-6- 10/20/2005(6) Ji-Sheng Chang
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Transcript of Q&A_-6- 10/20/2005(6) Ji-Sheng Chang
The Advanced Chemical Engineering Thermodynamics
Heat(q) and work(w) effects in a process and
internal energy(U) and enthalpy(H) at a change of states
Q&A_-6- 10/20/2005(6)
Ji-Sheng Chang
Equations of a substance
The ideal gas behavior of a fluid Volumetric equation:
PV=nRT, or PV=RT
Thermal equation: U=U(T), ordU=Cv(T)dT, and ΔU=∫Cv(T)dT;dH=Cp(T)dT, and ΔH=∫Cp(T)dT.
Equations for process calculations
Equations of work, heat, internal energy, and enthalpy for process calculations
1. The first law of thermodynamics for closed system… dU=dQirr.+dWirr.= dQrev.+dWrev.
2. Internal energy… dU=CvdT 3. Enthalpy… dH=CpdT 4. Work… dWrev.=-PdV 5. Heat flow… dQrev.=dU+PdV
Heat and work
Equations of work and heat for process calculations
1. Work …
2. Heat flow …
PdVR
CpVdP
R
CvdQ
V
dVRTCvdTdQ
P
dPRTCpdTdQ
V
dVRTdW
P
dPRTRdTdW
Isothermal process
Equations of work, heat, internal energy, and enthalpy for process calculations
ΔT=0; ΔU=∫Cv dT=0 ΔH=∫Cp dT=0
W=-PdV Q=W
Isobaric process
Equations of work, heat, internal energy, and enthalpy for process calculations
ΔH=∫Cp dT ΔU=∫Cv dT Q=ΔH W=ΔU-Q
Isochoric process
Equations of work, heat, internal energy, and enthalpy for process calculations
ΔH=∫Cp dT ΔU=∫Cv dT Q=ΔU W=0
Adiabatic process
Equations of work, heat, internal energy, and enthalpy for process calculations
Q=0 dU=W; CvdT=-PdV for ideal gas:
TVγ-1=constant TP(1-γ)/γ=constant PVγ=constant ; γ=Cp/Cv PV=RT; PV/T= constant
V
dVR
T
dTCv
Polytropic process
Equations of work, heat, internal energy, and enthalpy for process calculations
Polytropic process : PVσ=constant Isothermal process : σ=1 Isobaric process : σ=0 Isochoric process : σ=∞ Adiabatic process : σ=γ
Enthalpy change for a state change
Sensible heat effects of a change of states ΔH=∫Cp dT
Latent heats of pure substances Theoretical model
Empirical models
TCpdHTT 2
1
dT
dPVTH
sat
Standard enthalpy change
Standard heat of reaction ΔH(T0)rexa.
Standard heat of formation ΔH(T0)form.
Standard heat of combustion ΔH(T0)comb.
The heat of reaction
Temperature dependence of heat of reaction
ΔH(T)=ΔH(TT0)+ΔH(T0)+ΔH(T0 T) sensible heat
latent heat sensible heat