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**EGR 334 Thermodynamics Chapter 3: Section 11**

Lecture 09: Generalized Compressibility Chart Quiz Today?

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**Today’s main concepts:**

Universal Gas Constant, R Compressibility Factor, Z. Be able to use the Generalized Compressibility to solve problems Be able to use Z to determine if a gas can be considered to be an ideal gas. Be able to explain Equation of State Reading Assignment: Read Chap 3: Sections 12-14 Homework Assignment: From Chap 3: 92, 93, 96, 99

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Limitation: Like cp and cv, today’s topic is about compressible gases…. This method does not work for two phase mixtures such as water/steam. It only applies to gases. Compressibility Factor, Z where and

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**Universal Gas Constant**

R can also be expresses on a per mole basis: where M is the molecular weight (see Tables A-1 and A-1E) Substance Chem. Formula R (kJ/kg-K) R(Btu/lm-R) Air --- 0.2870 Ammonia NH3 0.4882 Argon Ar 0.2082 Carbon Dioxide CO2 0.1889 Carbon Monoxide CO 0.2968 Helium He 2.0769 Hydrogen H2 4.1240 Methane CH4 0.5183 Nitrogen N2 Oxygen O2 0.2598 Water H2O 0.4614

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**The constant R is called the Universal Gas Constant. **

Sec 3.11 : Compressibility The constant R is called the Universal Gas Constant. Where does this constant come from? For low pressure gases it was noted from experiment that there was a linear behavior between volume and pressure at constant temperature. then and the limit as P0 The ideal gas model assumes low P molecules are elastic spheres no forces between molecules

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**Define the compressibility factor Z,**

Sec 3.11 : Compressibility To compensate for non-ideal behavior we can use other equations of state (EOS) or use compressibility Define the compressibility factor Z, Z1 when ideal gas near critical point T >> Tc or (T > 2Tc) Step 1: Thus, analyze Z by first looking at the reduced variables Pc = Critical Pressure Tc = Critical Pressure

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Step 2: Using the reduced pressure, pr and reduced temperature, Tr determine Z from the Generalized compressibility charts. (see Figures A-1, A-2, and A-3 in appendix). Fig03_12

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**a) state whether the substance behaves as an ideal gas, if Z ≈ 1 **

Step 3: Use Z to a) state whether the substance behaves as an ideal gas, if Z ≈ 1 b) calculate the specific volume of the gas using where The figures also let’s you directly read reduced specific volume where

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**3) Calculate the missing property using**

Sec 3.11 : Compressibility Summarize: 1) from given information, calculate any two of these: (Note: pc and Tc can be found on Tables A-1 and A-1E) 2) Using Figures A-1, A-2, and A-3, read the value of Z 3) Calculate the missing property using where or (Note: M for different gases can be found on Table 3.1 on page 123.)

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Sec 3.11 : Compressibility Example: (3.95) A tank contains 2 m3 of air at -93°C and a gage pressure of 1.4 MPa. Determine the mass of air, in kg. The local atmospheric pressure is 1 atm. V = 2 m3 T = -93°C pgage = 1.4 MPa patm = MPa

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**Compressibility Figure**

Sec 3.11 : Compressibility Example: (3.95) Determine the mass of air, in kg V = 2 m3 T = -93°C = 180 K p = pgauge + patm = 1.4 MPa MPa = 1.5 MPa = 15 bar From Table A-1 (p. 816): For Air: 16) Tc = 133 K pc = 37.7 bar View Compressibility Figure Z=0.95

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**Equations of State: Relate the state variables T, p, V**

Sec : Equations of State & Sec 3.12 : Ideal Gas Model Equations of State: Relate the state variables T, p, V Ideal Gas Alternate Expressions When the gas follows the ideal gas law, Z = 1 p << pc and / or T >> Tc and

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**Equations of State: Relate the state variables T, P, V**

Sec : Equations of State & Sec 3.12 : Ideal Gas Model Equations of State: Relate the state variables T, P, V Ideal Gas Van der Waals b volume of particles a attraction between particles Redlich–Kwong Peng-Robinson virial B Two molecule interactions C Three molecule interactions

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Example: (3.105) A tank contains 10 lb of air at 70°F with a pressure of 30 psi. Determine the volume of the air, in ft3. Verify that ideal gas behavior can be assumed for air under these conditions. m = 10 lb T = 70°F p = 30 psi

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**Compressibility Figure**

Sec 3.12 : Ideal Gas Example: (3.105) Determine the volume of the air, in ft3. Verify that ideal gas behavior can be assumed for air under these conditions. For Air, (Table A-1E, p 864) Tc = 239 °R and pc = 37.2 atm m = 10 lb T = 70°F = 530°R p = 30 psi= 2.04 atm View Compressibility Figure Z= (Figure A-1)

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Example 3: Nitrogen gas is originally at p = 200 atm, T = K. It is cooled at constant volume to T = K. What is the pressure at the lower temperature? SOLUTION: From Table A-1 for Nitrogen pcr = 33.5 atm, Tcr = K At State 1, pr,1 = 200/33.5 = and Tr,1 = 252.4/126.2 = 2. According to compressibility factor chart , Z = vr' = 0.34. Following the constant vr' line until it intersects with the line at Tr,2 = 189.3/126.2 = 1.5 gives Pr,2 = 3.55. Thus P2 = 3.55 x 33.5 = 119 atm. Since the chart shows Z drops down to around 0.8 at State 2, so it would not be appropriate to treat it as an ideal gas law for this model.

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**End of Slides for Lecture 09**

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Speed of Gases. Speed of Gases Root Mean Square Speed of Gases R = J *K / mol J = 1kg * m2 / s2 MM = molar mass.

Speed of Gases. Speed of Gases Root Mean Square Speed of Gases R = J *K / mol J = 1kg * m2 / s2 MM = molar mass.

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