RT Constant Temperature. If the temperature throughout the gas remains constant (isothermal) at T=T then assuming the pressure at a reference location z= is p=Pa we have 32.2 Siratoghere 2-- or in (-z) or p p RT, Pa RT Trapee Appronimate tempeate distein he US Mandend mhene In a room filled with a gas, the variation of pressure with height is negligible. Tatm(z < 11km)=288.15-6.5Z gor2 (r+z)2 Air ASgh Advanced Thermodenamics s/23/2021 (By: MHJ Abyaneh) Show this for the following equation The variation of "g" with altitude based on the gravitational law: If go represents the absolute acceleration due to gravity at sea level, the absolute value at an altitude z is g- B0r+ z where r is the radius of the earth. gor? gor2 R(T, - bz)(r + z)² dP P. dz R(T- bz) dz where b = 6.5,z = elevation based on km & To = 288.15K Advanced Thermodynamics S/23/2021 (By: MHJ. Abyaeh) COMPRESSIBILITY FACTOR A MEASURE OF DEVIATION FROM IDEAL GAS BEHAVIOR The ideal-gas equation is very simple and thus very convenient to use. However, gases deviate from ideal-gas behavior significantly at states near the saturation region and the critica point. This deviation from ideal-gas behavior at a given temperature and pressure can accurately be accounted for by the introduction of a correction factor called the compressibility factor Z defined as: Z=1 ideal gas PR =Reduced pressure Pv Z = RT Z = Z(PR, TR) -Z<1 & Z>1 Real gas TR =Reduced temperature 1. At very low pressures (P, 2), ideal-gas behavior can be assumed with good accuracy regardless of pressure (except when P> 1). TA ldcal-gas bohavior Nonideal gas behavior 3. The deviation of a gas from ideal-gas behavior is greatest in the vicinity of the critical point Real P0 deal-gas hehavior gas