Changes Calculating of Enthalpy, Internal Energy, Volume For a Process of Interest
ChE 202 Spring 2010
Copyright 2010 D.B. Dadyburjor and J. A. Shaeiwitz
Calculating Changes of Enthalpy, Internal Energy, Volume
H , U , V
Why do I care? So we can use these in (MB,) EB:
- - (vsys2)/2 + g zsys + U sys
0 = etc
= Q(in)/msys Ws(by)/msys Pext Vsys
& & ( H i + E k ,i + E p,i )mi ( H i + E k ,i + E p,i )mi + Q& (in) W&s(by) in out
Copyright 2010 D.B. Dadyburjor and J. A. Shaeiwitz
Calculating Changes of Enthalpy, Internal Energy, Volume - 2
H , U , V
For V(T,P), Can calculate absolute value,
or can use data sources For H and U, Can calculate M = M(T2,P2) M(T1, P1) Or can use data sources Value of H(T,P) read off is actually H(T,P) H(Tref, Pref) Get U from H = U + PV
Make sure different data sources have the same reference states
Data sources first, then calculations
Copyright 2010 D.B. Dadyburjor and J. A. Shaeiwitz
Sources of Data
Steam tables/other tables
advantages
much data, wide range of conditions
disadvantage
specific species (e.g., water) need for interpolation
Diagrams (like P H diagrams)
advantage
good for quick calculations
disadvantage
not accurate
Copyright 2010 D.B. Dadyburjor and J. A. Shaeiwitz
Sources of Data - 2
Perrys Handbook the ChE data bible
It also contains instructional material We have hard copies, and PDF version is on all computers
advantage
it contains most ChE information ever needed
disadvantage
sometimes hard to find what you want until you know your way around it
Copyright 2010 D.B. Dadyburjor and J. A. Shaeiwitz
Sources of Data - 3
CD accompanying book (and similar data bases)
advantage
has huge amount of information no need for interpolation
disadvantage
not always near computer
Chemcad
advantage
has huge data base
disadvantage
too costly for individual use, data not always in user-friendly format
Copyright 2010 D.B. Dadyburjor and J. A. Shaeiwitz
Calculating H, U in general
For an arbitrary process Break up process into sub-processes Calculate (M) for each Then Mprocess = M1 + M2 + Can do this because H and U are State Functions (path-independent)
Copyright 2010 D.B. Dadyburjor and J. A. Shaeiwitz
Calculating H, U in general -- 2
What sorts of sub-processes? Simple ones
Change in pressure at constant temperature Change in temperature at constant pressure Change in T or P at constant volume Change in phase at constant P and T Mixing of pure components to multicomponent system at constant T and P (and reverse) Pure components in stoichiometric amounts reacting to form pure products(s)
Copyright 2010 D.B. Dadyburjor and J. A. Shaeiwitz
Calculating H, U in general -- 3
Examples (multiple paths possible)
Ice at -5C, 1 atm -> Steam at 300C, 5 atm
(Water at 30C, 1 atm) + (NaCl at 25C, 1 atm) -> Saline solution at 50C, 1 atm
Copyright 2010 D.B. Dadyburjor and J. A. Shaeiwitz
Calculating M for P at constant T (P)T
For Ideal Gases, U IG so ( U ) IG T Now Then 0 = U (T ) not P H IG U IG + ( PV ) IG = U IG + ( RT ) H IG = H (T ) not P 0
so ( H ) IG T
For Real Gases, correlations with Z, etc, but (IG) ok upto P Pc For liquids and solids, U and H are ~ independent of P (but PV RT !) correlations (later)
Copyright 2010 D.B. Dadyburjor and J. A. Shaeiwitz
Calculating M for T at constant P (T)P
At constant P, can show that
T2 H = H (T2 , P ) H (T1, P ) = T1
C p dT
where Cp is the specific heat at pressure constant Then
T2 U = H ( PV ) =
C p dT P {V2 V1}
T1
Copyright 2010 D.B. Dadyburjor and J. A. Shaeiwitz
Calculating M for T at constant V (T)V
At constant V, can show that
T2 U = U (T2 , V ) U (T1, V ) = T1
Cv dT
where Cv is the specific heat at constant specific volume Then
T2 H = U + ( PV ) =
Cv dT + V {P2 P } 1
T1
Copyright 2010 D.B. Dadyburjor and J. A. Shaeiwitz
Heat Capacity Integrals
C p tabulated for (s), (l), (v) as f(T); see, for example, Table B.2, p. 635 C p = a + bT + cT 2 + dT 3 T2 H =
( a + bT + cT 2 + dT 3 )dT
T1 Must use form and units indicated
Or can estimate by Kopps rule (Table B.10, p. 653)
Cv: For IG, Cp Cv = R => Cv = (a R) + bT + cT2 + dT3 For non-ideal gases, generally a good approximation upto Pc (better estimates in Thermodynamics) For (l), (s): Cv ~ Cp Copyright 2010 D.B. Dadyburjor and J. A. Shaeiwitz
Calculating M for at constant T and P
H = H (2 , T , P ) H (1, T , P ) = H
-- Latent heat of phase change, a measurable quantity
U = H ( PV ) = H P(V [2 , T , P ] V [1, T , P ]) 2 = ( v ), 1 = (l ) H vap , latent heat of vaporization 2 = (l ), 1 = ( s ) H fus , latent heat of fusion 2 = ( v ), 1 = ( s ) H sub , latent heat of sub lim ation
Can show that, at constant T & P,
Copyright 2010 D.B. Dadyburjor and J. A. Shaeiwitz
Calculating M for at constant T and P - 2
H: Estimate, or use data sources
Data sources: Table B-1 in F&R Other sources as described earlier
Estimates: Use P*(T) data Clausius-Clayperon -> ln[P*] = - {H*/(RT)} + B For vaporization Troutons Rule Chens Equation Watsons Rule
For fusion as f (Tm) Generally tabulated only at 1 atm, T2 (normal boiling point, etc.) At other T,P values - use sub-processes
Copyright 2010 D.B. Dadyburjor and J. A. Shaeiwitz
Example not at normal bp
What is Hv for water at 200C (same as H for water from liquid to vapor at 200C)?
only Hv at normal boiling point is tabulated take advantage of enthalpy as state function H for this change in state Hv (200C)
200C vapor
T2 Tb
200C liquid
Tb
Cp
L
dT
T1
C p dT
v
100C liquid
Hv (normal bp)
100C vapor
is the sum of H values for these three changes in state
Copyright 2010 D.B. Dadyburjor and J. A. Shaeiwitz
Example not at normal bp
What is Hv for water at 200C?
200C liquid
Tb
Hv (200C)
200C vapor
Cp
T2 Tb
L
dT
T1
C p dT
v
100C liquid
Hv (normal bp)
100C vapor
100
H =
C pL dT + H v (Tnbp ) + C pv dT
100
positive numbers Copyright 2010 D.B. Dadyburjor and J. A. Shaeiwitz negative number
200
200
Enthalpy Changes for Phase Transitions general result
H L V = C pL dT + H v + C pv dT
T1
take from initial T to boiling point vaporize
Tb
T2 Tb
take from boiling point to final T
If T1 = T2, this is Hv at T1 = T2
If T1 T2, this is H between liquid at T1 and vapor at T2 For condensation, reverse signs If going from (s) to (v), add fusion enthalpy and another integral
Copyright 2010 D.B. Dadyburjor and J. A. Shaeiwitz
this is what is meant by a state function
Sub-processes considered to date
Change in pressure at constant temperature Change in temperature at constant pressure Change in T or P at constant volume Change in phase at constant P and T Mixing of pure components to multicomponent system at constant T and P (and reverse) Pure components in stoichiometric amounts reacting to form pure products(s)
Copyright 2010 D.B. Dadyburjor and J. A. Shaeiwitz