Thermodynamics filled in class notes_Part_43

# Thermodynamics filled in class notes_Part_43 - 93 3.3....

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 93 3.3. IDEAL MIXTURES OF IDEAL GASES k= cP , cv (3.236) N yi si = sM, s= (3.237) i=1 ρi , Mi v 1 V = = = vi Mi , = ni yi ρi V ∂V = = v = vM , = ∂ni P,T,nj n ρ i = yi ρ = (3.238) vi (3.239) vi (3.240) if ideal gas Pi = yi P, (3.241) P = ρRT = RT , v (3.242) if ideal gas Pi = ρi RT = RT , vi (3.243) if ideal gas P = u + P v = u + RT = hM, ρ h = u+ (3.244) if ideal gas hi = o hi , if ideal gas, hi = ui + (3.245) Pi = ui + Pi v i = ui + P vi = ui + RT = hi Mi , ρi (3.246) if ideal gas T o hi = h298,i + ˆˆ cP i(T ) dT = hi Mi , (3.247) 298 if ideal gas T si = so ,i 298 + 298 ˆ cP i (T ) ˆ dT −R ln ˆ T yi P , Po (3.248) =s o T,i if ideal gas yi P Po si = so − R ln T,i = si Mi , (3.249) if ideal gas N T yi so ,i 298 s= i=1 + 298 ˆ c P (T ) ˆ dT − R ln ˆ T P Po N − R ln y yi i = sM. i=1 if ideal gas (3.250) CC BY-NC-ND. 18 November 2011, J. M. Powers. 94 CHAPTER 3. GAS MIXTURES 3.3.3 Amagat model The Amagat model is an entirely diﬀerent paradigm than the Dalton model. It is not used as often. In the Amagat model, • all components share a common temperature T , • all components share a common pressure P , and • each component has a diﬀerent volume. Consider, for example, a binary mixture of calorically perfect ideal gases, A and B . For the mixture, one has P V = nRT, (3.251) with n = nA + nB . (3.252) P VA = nA RT, P VB = nB RT. (3.253) (3.254) PV P VA P VB = + . RT RT RT (3.255) For the components one has Then n = nA + nB reduces to Thus V = VA + VB , VA VB + . 1= V V 3.4 (3.256) (3.257) Gas-vapor mixtures Next consider a mixture of ideal gases in which one of the components may undergo a phase transition to its liquid state. The most important practical example is an air-water mixture. Assume the following: • The solid or liquid contains no dissolved gases. • The gaseous phases are all well modeled as ideal gases. • When the gas mixture and the condensed phase are at a given total pressure and temperature, the equilibrium between the condensed phase and its vapor is not inﬂuenced by the other component. So for a binary mixture of A and B where A could have both gas and liquid components PA = Psat . That is the partial pressure of A is equal to its saturation pressure at the appropriate temperature. CC BY-NC-ND. 18 November 2011, J. M. Powers. ...
View Full Document

## This note was uploaded on 11/26/2011 for the course EGN 3381 taught by Professor Park-sou during the Fall '11 term at FSU.

Ask a homework question - tutors are online