Single Phase Systems Measured Data from an existing process (experiments!) Process Specifications/Design Physical Properties/Laws Use physical laws as additional relations to lower the number of degrees-of-freedom.

Single Phase Systems Liquid and Solid Densities -solids and liquids are essentially incompressible you can use the density at one T and P for almost any other T and P Gas Densities -the density is obtained by using an equation of state. An equation of state relates the molar density (or specific molar volume) of a fluid to the temperature and pressure of the fluid

Single Phase Systems simplest Equation of State Ideal Gas Law : PV=nRT - R = universal gas constant - 10.73 (psia)(ft3)/(lb-mol)(oR) - 8.314 (kPa)(m3)/(kg-mol)(K) - 82.06 (cm3)(atm)/(g-mol)(K) - 0.7302 (ft3)(atm)/(lb-mol)(oR) Standard Temperature and Pressure (STP) -an arbitrary reference point chosen to be T = 273K (0oC) and P = 1 atm - volume of 1 g-mol of ideal gas at STP is 22.415 li.

Ideal Gas Law Generally works for:) RT if V = > 5 L/mol (80 ft 3 / lb - mol) diatomic gases Pif V

RT 3 == > 20 L/mol (320 ft / lb - mol) other gases P

STP Conversion from standard conditions: no need to use R SCM, SCF SCMH and SCFH

Single Phase Systems Ideal Gas Mixtures Partial pressure of component A refers to the pressure that would be exerted by nA moles of A alone in the same total volume V at the same pressure P. - for a mixture of n moles ideal gases A, B, C, at pressure P and temperature T occupying total volume V. pA (partial pressure of A) = nART/V pA + pB + pC .= (nA + nB + nC +..)RT/V = nRT/V =P - Daltons Law of Partial Pressures pA/P = nA/n = yA pA = yAP

Single Phase Systems Ideal Gas Mixtures Pure component volume of A (vA) refers to the volume that would be occupied by nA moles of A alone at the total pressure P and temperature T of the mixture PvA = nART vA/ V = nA/ n =yA vA = yAV V = vA + vB + .

Single Phase Systems Example: An ideal gas mixture contains 40% N2, 30% CO, and 30% H2 by volume at P=2 atm(absolute) and T = 65oC. Calculate; a.) the partial pressure of each component b.) the mass fraction of N2 c.) the average molecular weight of the gas d.) the density of the gas (g/liter)

Single Phase Systems Example: An adult takes 12 breaths per minute inhaling roughly 500 ml of air with each breath. The molar compositions of the inspired and expired gases are as follows:Species Inspired Gas Expired Gas

O2 CO2 N2 H2O

20.6 0.0 77.4 2.0

15.1 3.7 75 6.2

Single Phase SystemsThe inspired gas is at 24oC and 1 atm, and the expired gas is at body temperature and pressure ( 37oC and 1 atm). Nitrogen is not transported into or out of the blood. a.) calculate the masses of each O2, CO2 and H2O transferred from the pulmonary gases to the blood or vice versa. b.) calculate the volume of air exhaled per millimeter inhaled c.) at what rate (g/min) is this individual losing weight by merely breathing.

Single Phase Systems Example: Spray drying is a process in which a liquid containing dissolved or suspended solids is injected into a chamber through a spray nozzle or centrifugal disk atomizer. The resulting mist is contracted with hot air, which evaporates most or all of the liquid, leaving the dried solids to fall to the conveyor belt at the bottom of the chamber. Powdered milk is produced in a spray dryer 6 m in diameter by 6 m high. Air enters at 167oC and -40 cm H2O. The milk fed to the atomizer contains 70 wt % water by mass all of which evaporates. The outlet gas contains 12 mol% water and leaves the chamber at 83oC and 1atm(absolute) at a rate of 311 m3/min. Calculate the production of dried milk and the volumetric flowrate of the inlet air

Single Phase Systems Non-Ideal Equations of State An equation of state relates the molar density (or specific molar volume) of a fluid to the temperature and pressure of that fluid 1.) Virial Equations of State

where B, C, and D (etc.) are material dependent constants

Single Phase Systems Truncated Virial Equation

valid for non-polar gases Cubic Equations of State 1. van der Waals Equation

Single Phase Systems Compressibility Factor and Corresponding States compressibility factor, z, is a dimensionless number that represents a material's deviation from ideal gas behavior The "law" at corresponding states suggests that gases behave similarly depending on how far from their critical point they are. Determination of z: a.) Determine Pc and Tc for He and H, Tc and Pc must be adjusted by: Tc = Tc + 8K ; Pc = Pc + 8 atm

Single Phase Systemsc.) Calculate reduced values of variables; Tr = T/ Tc ; Pr = P/Pc Vr = V /(RTc/Pc) = VPc/RTc d.) Use the compressibility chart to determine z.

Single Phase Systems Non-ideal Gases- errors in ideal gas predictions become most striking as one approaches the gases critical conditions At higher temperatures and/or higher pressures the difference between a gas and a liquid eventually disappears(!) and a supercritical fluid is formed. The point at which this happens is called the critical point A supercritical fluid is a substance which is above its critical temperature, Tc and pressure, Pc.

Single Phase Systems Real Gas Mixtures: Kays Rule PV = zmnRT or PV = zmRT where zm = mean compressibility factor To determine zm, use pseudo-critical Pseudocritical temperature: Tc = yaTca + ybTcb + ycTcc .. Pseudocritical pressure: Pc = yaPca + ybPcb + ycPcc Pseudoreduced Parameters Pr = P/ Pc Tr = T/ Tc

Single Phase Systems Example: A stream of oxygen enters a compressor at 298K and 1.00 atm at a rate of 87m3/h and is compressed to 358 K and 1000 atm. Calculate the flowrate of compressed O2 using the compressibility factor equation of state.

Single Phase Systems Example: The product gas from a coal gasification plant consists of 60 mole % CO and the balance H2; it leaves the plant of 150oC and 2000 psia. The gas is expanded through a turbine and the outlet gas is fed to a boiler furnace at 100oC and 1 atm at the rate of 20,000 ft3/min. Estimate the inlet flowrate to the turbine in ft3/min, using Kays Rule? What percentage error would result from the use of the ideal gas law at the turbine inlet?