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