Lec 7: Property tables, ideal and real gases

For next time: Outline: Important points: Read: § 3-8 to 3-12 HW4 due EES Quality, internal energy, enthalpy Real gases Important points: How to use the quality to find properties of mixtures How to evaluate a given process in a property diagram How to calculate and apply corrections to the IGL for real gases

TEAMPLAY Find, for water, the following properties: the saturation pressure at a saturation temperature of 100 F. and find the saturation temperature at a pressure of 6 MPa. Make sure everyone in your group understands how to do this.

Quality We often represent the relative amount of vapor present by something called the quality x.

Quality is related to the horizontal differences of P-V and T-v diagrams

What is the new v?

So... v = (1-x)vf + xvg = vf + x(vg - vf) or, writing vfg  vg – vf v = vf + xvfg

Obtaining u in the vapor dome What you do for v works for u (and for other things) u = (1-x)uf + xug = uf + x(ug - uf) = uf + xufg

A new property: enthalpy, H Enthalpy is simply the sum of the internal energy, U, and the pressure volume product, pV H  U + pV Now,

Enthalpy--the bottom line H = U + pV h = u + pv h = (1-x)hf + xhg = hf + x(hg - hf) = hf + xhfg

The P-V or P-v plane For the next few lectures we will often look at the two dimensions P and v, or P and V. The P is always on the ordinate and the v is always on the abcissa, just opposite to the familiar x-y plane.

Subcooled or Compressed Liquid Region Sat. Vapor Line Sat. Liquid Line Subcooled or Compressed Liquid Region Sat. Vapor Line Superheated Region - 100% Vapor Two-Phase or Saturation Region - gas and liquid coexist

For water p v superheated region Table Page A-6 940/43 A-6E 986/88 If T=Tsat, P  Psat If P=Psat, T >Tsat superheated region Table Page A-7 944 A-7E 989 If T=Tsat PPsat. If P=Psat, TTsat. subcooled or compressed liquid region Table Page A-4 936/7 A-5 938/9 A-4E 982/3 A-5E 983/4 saturation region P=Psat and T=Tsat v

Superheat tables--compressed liquid tables are similar

TEAMPLAY Complete the table below as a team. The substance is water. Make sure everybody understands how to do it!

TEAMPLAY A container holds 1 kg of liquid water and 1 kg of steam in equilibrium at 0.7 MPa. What is the temperature of the mixture in C? If we hold the pressure constant and increase the temperature to 320 C, what is the change in volume? Show the process on the Pv diagram.

Sample Problem Compare the values of the specific volume of water at saturated liquid conditions and 100C with the values of specific volume at of water at saturated liquid conditions and 100C and the following pressures: 5, 20, and 30 MPa. What conclusions can be drawn from the comparison?

SOLUTION From compressed liquid tables

What can we learn? IMPORTANT!! Specific volume is approximately constant over large changes in pressure if T=C Liquid does not change specific volume significantly as pressure is changed…it can’t be “compressed” When compressed liquid tables are not available, estimate property data at sat. liquid conditions at the same temperature as the compressed liquid. IMPORTANT!!

Consider R-134a (Refrigerant 134a) We can make a diagram for this as we did for water but there is no data in the compressed or subcooled liquid region.

For R-134a superheated region P v If T=Tsat, PPsat Table Page A-13 950/1 A-13E 995/6 If T=Tsat, PPsat If P=Psat, T>Tsat superheated region P Table Page A-11 (T) 948 A-11E(T) 993 A-12 (P) 949 A-12E(P) 994 saturation region P=Psat and T=Tsat v

R-134a IS NOT AN IDEAL GAS!

TEAMPLAY What is the specific volume of saturated liquid R-134a @ 0 °C? What is the internal energy at -10 °C and 0.14 MPa? What is the pressure at x = 0.1 and 0 °F? What is h at the same conditions?

TEAMPLAY Under what conditions is it appropriate to apply the ideal gas equation of state?

Ideal gas “law” is a simple equation of state Ru = universal gas constant = 8.3144 kPa•m3/kmol•K = 1.545 ft • lbf/lbmol•R

Molar mass or molecular weight is sometimes confusing Take air as an example:

Specific gas constant Universal gas constant given inside back cover of your textbook Specific gas constant calculated by dividing universal gas constant by molar mass

Percent error for applying ideal gas equation of state to steam

Real gases Pv = ZRT, or Pv = ZRuT, where v is volume per unit mole. Z is known as the compressibility factor

Principle of corresponding states “The compressibility factor Z is the same for all gases at the same values of the reduced temperature and reduced pressure.”

Compressibility factor What is it really doing? It accounts mainly for two things: Molecular structure Intermolecular attractive forces

Reduced properties Where: PR and TR are reduced values. Pc and Tc are critical properties.

Where do you find critical properties? Look in the appendices of your text book. For the SI system they are on p. 930 in Table A-1, along with molar mass. For USCS system, they are on p. 976 in Table A-1E

Reduced properties This works great if you are given a gas, a P and a T and asked to find the v. However, if you are given P and v and asked to find T (or T and v and asked to find P), you can use the pseudoreduced volume.

Reduced properties In those cases use the pseudoreduced volume:

Compressibility factor It is shown in Figure 3-56 (p. 100) in terms of actual experimental data

Compressibility factor for ten substances

TEAMPLAY Use the compressibility factor to determine the error in treating oxygen gas at 160 K and 3 MPa as an ideal gas.