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Mixtures and Solutions: 

Mixtures and Solutions Harold Schock Michigan State University College of Engineering Fall 2007 - ME444

Mixtures of Ideal Gases: 

The mole fraction yi of component i is defined as   ni = no. of moles of i n = total moles in mixture   Similarly mass fraction   mi = mass of component i m = total mass in mixture Mixtures of Ideal Gases

What Properties Can We Measure?: 

What Properties Can We Measure?   We could have tables to determine the properties of the mixture, but we would prefer to be able to derive properties from the pure substances that comprise the mixture.

Slide4: 

One Exception: Air tables which are based on the following composition:   %MoleBasis   Nitrogen 78.10 Oxygen 20.95 Argon 0.92 CO2+trace 0.03

Slide5: 

In general, properties of mixtures are defined as partial molal properties.   For example let’s examine the internal energy of the gases A + B shown above     where denotes the partial molal internal energy. Similar equations can be developed for other properties.

Slide6: 

Two models are used in conjunction with mixtures of gases, namely the Dalton Model and the Amagat Model. Dalton Model: Properties of each component are considered as each component existed separately at the volume and temperature of the mixture.

Dalton Model: 

Dalton Model

Ideal Gas Dalton Model : 

Ideal Gas Dalton Model   Mixture: n=nA+nB   Components: Using Ideal Gas: n=nA+nB   or P=PA+PB  where PA and PB are called partial pressures.

Slide9: 

Amagat Model: The properties of each component are evaluated as though each component existed separately at the pressure and temperature of the mixture as shown in the figure.

Slide10: 

Mixture: n=nA+nB   Components:   n=nA+nB   or or V=VA+VB   and are called volume fractions. Ideal Gas Amagat Model

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One can shown based on above that     Using the Dalton model we can continue, (each component occupies entire volume)   Since for ideal gases u,hu(T) and h(T) only      

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are given in per mole pure A,B. The entropy of an ideal gas is a function of T and P   entropy/mole at T and PA   = entropy/mole at T and PB

Slide13: 

H2O-Air Mixtures Assumptions: 1. Solid or liquid phase has no dissolved gases. 2. Gaseous phase can be treated as a mixture of ideal gases. 3. When the mixture and the condensed phase are at a given T, the equilibrium between the condensed phase and its vapor do not influence each other. 

Slide14: 

Dew Point: The “dew point” of a gas-vapor mixture is the temperature at which the vapor condenses when it is cooled at constant pressure.   If the vapor is at the saturation pressure and temperature, the mixture is called a “saturated mixture” or “saturated air”.

T-s Diagram for H2O: 

T-s Diagram for H2O T s

Slide16: 

Relative Humidity  In terms of the previous diagram Since we are considering vapor to be an ideal gas

Slide17: 

Humidity ratio (w) of an air-water vapor mixture Since both the water vapor, air and mixture to be ideal gases and

The Adiabatic Saturation Process: 

The Adiabatic Saturation Process If 1 < 100%, H2O liquid will evaporate and temperature of air-vap mixture will decrease If a) Mixture leaving 2 is saturated b) Process is adiabatic c) Pressure is approximately constant Saturated-Vapor Mixture Air & Vapor Water

Slide19: 

Then, temperature on the mixture @ 2 is called the adiabatic saturation temperature. In a SSSF process, H2O liquid is added Neglectivity changes in ICE and PE the first law for the SSSF System is: Saturated-Vapor Mixture Air & Vapor Water

Wet-Bulb / Dry Bulb Temperature: 

Wet-Bulb / Dry Bulb Temperature Humidity is usually found from dry bulb, wet bulb data Continuous-flow psychrometer Sling psychrometer

Slide22: 

How does the wet bulb temperature change? If air-water vapor mixture is not saturated water on the wick starts to evaporated and this vapor diffuses into the air Velocity air > 3 m/s

Slide24: 

T of water in wick will drop because of the evaporation Heat is transferred from the thermometer and the air, and T therm. Drops Eventually, a steady rate will be reached How does the wet bulb temperature change, continued

Slide25: 

Difference Between “Wet Bulb” and “Adiabatic Saturation Temperature (AST) Wet Bulb: influenced by heat and mass transfer AST: involves equilibrium between the entering air-vapor mixture and water at the AST However, for water-vapor mixtures at atmospheric T, P the AST WBT – Not necessarily true at Ts and Ps significantly different from ATMOSPHERIC CONDITIONS

Summary: 

Dalton Model Volume & temperature constant, leads to the concept of partial pressures Amagat Model Pressure and temperature constant, leads to the concept of volume fractions Summary

Summary, (cont.): 

Summary, (cont.) Concepts of and Dew Point Have been introduced and their relationship formulated Adiabatic saturation process allows one to easily measure the humidity of an air-vapor mixture

Example problem 3.1-1.Two insulated tanks A and B are connected by a valve. Tank A initially contains oxygen at 400kPa and 100C. and has a volume pf 10m3. Tank B initially contains nitrogen at 200kPa and 500C and has a volume of 10m3. The valve is opened and remains open until the mixture comes to a uniform state. Determine the final temperature and pressure and the entropy change for the system.: 

Example problem 3.1-1. Two insulated tanks A and B are connected by a valve. Tank A initially contains oxygen at 400kPa and 100C. and has a volume pf 10m3. Tank B initially contains nitrogen at 200kPa and 500C and has a volume of 10m3. The valve is opened and remains open until the mixture comes to a uniform state. Determine the final temperature and pressure and the entropy change for the system. 2m3 10m3 TA1 = 100C TB1 = 500C PB1 = 200kPa B = Nitrogen A = Oxygen PA1 = 200kPa A B 2m3 10m3 T

System: Tank boundariesWhat is known? Tanks are insulated  ,and no work has been done: 

System: Tank boundaries What is known? Tanks are insulated ,and no work has been done First Law: U2 – U1 = 0 or EP 3.1.2 02 02 A1 N2 VN2 2 B1 2